How do you solve this? | Mathematics | Page 1

iron cape Oct 12, 2023, 5:48 PM

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I have a horrible maths teacher which does not explain anything well imo if anyone could explain how to solve this or has any videos on these problems please paste the link or share them any help is appreciated thank you

tame hingeBOT Oct 12, 2023, 5:48 PM

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little gulch Oct 12, 2023, 5:55 PM

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Have you tried to expand the numerator using

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$(a-b)^2 = a^2-2ab+b^2$

placid wraithBOT Oct 12, 2023, 5:56 PM

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Daddy_314

iron cape Oct 12, 2023, 5:58 PM

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I know you can change the square root squared to 1/2 as a power I think I tried that but it didn't get me anywhere yet

little gulch Oct 12, 2023, 6:00 PM

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Dont panic

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Just try to apply this formula step by step

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Taking a = 2
And $ b = \sqrt{x}$

What is $a^2$ ?
What is $b^2$ ?

placid wraithBOT Oct 12, 2023, 6:00 PM

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Daddy_314

little gulch Oct 12, 2023, 6:01 PM

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What is $2ab$

placid wraithBOT Oct 12, 2023, 6:01 PM

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Daddy_314

iron cape Oct 12, 2023, 6:02 PM

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A² would be 4 and B² would be X? Since you're squaring rhe Square root?

little gulch Oct 12, 2023, 6:04 PM

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Very good

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So can you recap what the numerator is

iron cape Oct 12, 2023, 6:06 PM

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4-x?

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4-4√x+x?

little gulch Oct 12, 2023, 6:25 PM

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Yes !

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Now you need to remember the property that says:

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$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$

placid wraithBOT Oct 12, 2023, 6:26 PM

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Daddy_314

little gulch Oct 12, 2023, 6:26 PM

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Do you remember this property ?

iron cape Oct 12, 2023, 6:27 PM

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I dont remember the property which states this sorry

little gulch Oct 12, 2023, 6:27 PM

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It says:
If you add two numbers (for example 4 and 10) and then divide the sum by a number say 2 the result (14/2=7) would be the same if you had divided 4 by 2 and then 10 by 2 and added the results separately

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Because 4/2 + 10/2 = 2 + 5 = 7

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The same as (10+4)/2

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= 14/2 = 7

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This is a simple property

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That we can use here

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But instead of having (a+b)/c

We have (a+b+c)/d

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But the same is true

iron cape Oct 12, 2023, 6:29 PM

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Oh ok

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But how would we use it here?

little gulch Oct 12, 2023, 6:30 PM

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iron cape 4-4√x+x?

You found this

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Now divide each term by sqrt(x)

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We are trying to simplify the fraction a little bit

iron cape Oct 12, 2023, 6:31 PM

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So 4-4√x+x divided by √x?

little gulch Oct 12, 2023, 6:31 PM

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$\frac{4-4\sqrt{x} + x}{\sqrt{x}}$

$= \frac{4}{\sqrt{x}} + \frac{-4 \sqrt{x}}{\sqrt{x}} + something $

placid wraithBOT Oct 12, 2023, 6:32 PM

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Daddy_314

little gulch Oct 12, 2023, 6:32 PM

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Can you guess what something is

iron cape Oct 12, 2023, 6:33 PM

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Something would be +X?

little gulch Oct 12, 2023, 6:34 PM

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We need to divide each term in the numerator by $\sqrt{x}$

placid wraithBOT Oct 12, 2023, 6:34 PM

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Daddy_314

iron cape Oct 12, 2023, 6:34 PM

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How would you go about divided 4 by the square root of a value I dont know the value of?

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I dont understand that

little gulch Oct 12, 2023, 6:37 PM

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We don't know the value of the square root of x, you are right

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But no one asked to find a value

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The original question was to rewrite the first expression into another form (the second one)

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Both are not given numbers

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We are manipulating the first expression

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In order to transform it into another one that is equal to it

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For all values of x

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Imagine I told you to simplify

(2x/x)
Although you dont know x, you can simplify this and say it is equal to "2"

iron cape Oct 12, 2023, 6:39 PM

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Oh because you remove x from both sides?

little gulch Oct 12, 2023, 6:39 PM

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Or (ab/a) is equal to b although you know neither a nor b

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But you can say the two expressions are equal

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Because you used rules of algebra

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To transform the expression

iron cape Oct 12, 2023, 6:40 PM

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But how do we do 4/x sq root?

little gulch Oct 12, 2023, 6:41 PM

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We dont do anything to it

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It stays as it is

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Because we need to remember that

$\sqrt{x} = x^{\frac{1}{2}}$

placid wraithBOT Oct 12, 2023, 6:42 PM

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Daddy_314

little gulch Oct 12, 2023, 6:42 PM

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Why ? Well because as you have said, square root of x squared gives x

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And also $(x^{\frac{1}{2}})^2 = x^{\frac{1}{2} \times 2} = x^1 = x$

placid wraithBOT Oct 12, 2023, 6:43 PM

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Daddy_314

little gulch Oct 12, 2023, 6:43 PM

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So both of these numbers have the same square

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They are indeed equal

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If you forgot these, it is okay

iron cape Oct 12, 2023, 6:43 PM

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placid wraith **Daddy\_314**

So do we just need to find something?

little gulch Oct 12, 2023, 6:44 PM

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Yes

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I will let you think a bit

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It's not a difficult exercise

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But you need some revisions

iron cape Oct 12, 2023, 6:44 PM

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Do you know any videos which would help on these rules?

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I haven't done them in a while

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Would something be X/Square root of X?

little gulch Oct 12, 2023, 6:50 PM

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Yes !

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And you can simplify it a little bit

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I think you just need to review some basic properties (these exercises are a great opportunity for you to review all the properties)

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Try to take some notes

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On a separate notebook

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Of each property

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You will see that eventually, you will have them all in your notebook

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These exercises are good only if you try to learn each step and take notes

iron cape Oct 12, 2023, 6:53 PM

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Oh ok

little gulch Oct 12, 2023, 6:54 PM

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When I was in school, I would redo all the exercises every week from the beginning of the chapter

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This is how I always aced the math exams

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And if I struggled I would ask

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But then Id learn the trick a second and third time

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Dont be discouraged

iron cape Oct 12, 2023, 6:56 PM

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Thanks

iron cape Oct 12, 2023, 6:59 PM

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placid wraith **Daddy\_314**

Is this the answer to the problem by the way? Including the X/square root of x

little gulch Oct 12, 2023, 7:23 PM

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No

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It is not done

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You need to conclude...

iron cape Oct 13, 2023, 6:00 AM

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So I need to turn thr fractions into numbers?

little gulch Oct 13, 2023, 6:36 AM

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Do you understand the original question?

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Show that "something" can be written as "something else"

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No one asked to turn something into numbers

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You need to arrive from the first form to the second form

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By using the rules we talked about

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The two forms look different but are equal

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For all values of x that you would choose

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But no one asked you to choose a particular x

iron cape Oct 13, 2023, 6:40 AM

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Just by the rules we used before?

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I'm in year 9 some things I didnt learn last year

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Sorry If I don't understand some stuff

little gulch Oct 13, 2023, 9:48 AM

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iron cape Just by the rules we used before?

Yes

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All the needed rules are in this conversation

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You don't need anything extra

autumn kayak Apr 12, 2024, 11:48 PM

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.close

#How do you solve this?