A Rational Numbers Question I Cant Solve

[vernal flare]

Can you please explain me the solving steps for this question I would appreciate it.

[honest carbon]

A Rational Numbers Question I Cant Solve

[misty tusk]

First thing that you want to do is simplify the expression on the bottom

[edgy rampart]

hmm

[misty tusk]

i.e $\dfrac{x-2}{x}=1-\dfrac{2}{x}$

[magic axle]

catman

[edgy rampart]

maybe take the LCM as [xyz] then multiply both sides by it?

or wait

can we cross multiply [(x-2)/x + (y-4)/y]

[misty tusk]

we don't need to do any multiplication

simplify the expression first

[edgy rampart]

hmm, like how are we gonna simplify it?

[misty tusk]

@edgy rampart

[edgy rampart]

I am not getting it

[misty tusk]

the x-2/x term can be simplified

to 1-2/x

do that for each term

[edgy rampart]

how did they get x-2/x?

[misty tusk]

(x-2)/x is in the question

[edgy rampart]

oh I thought it was the next step or something

hmm yea we can simplify like that, as we gett [x/x - 2/x]

[vernal flare]

did I simplify correctly

[chilly palm]

thats easy bruv

[misty tusk]

double check your simplification of the z term

[misty tusk]

no one asked

[vernal flare]

hm there should be a minus next to 6 right?

[misty tusk]

yes

it should be -3-6/z

[vernal flare]

understood, now that we simplified the expressions what do we do next?

[misty tusk]

well you can start by combining the like terms

so move your constants to the side and calculate them

so 1+1-3

[vernal flare]

Ok so the numerator equals -1

[misty tusk]

what does your equation look like now

[vernal flare]

its just -1

[misty tusk]

what about the rest of your terms?

[vernal flare]

the top terms are each multiplied by 2

the one that equals 7

[misty tusk]

thats a good observation

write it out as a step and show it here

[misty tusk]

alright, so now for the expression on the bottom

what does that look like

[vernal flare]

These are the two answers I got from both fraction expressions so I add the two answers together

[misty tusk]

this is correct, now make sure that we can clearly label each of your steps

that way you can get full credit

[vernal flare]

Ok I simplify the fraction expressions bellow and add the whole numbers together and I get the result -1

Then I place the above fraction into a parenthesis and multiply the number 2 on each side

Then I add both -1 and -14

[misty tusk]

yes

it should look like
$$
\begin{align*}
\dfrac{x-2}{x}+\dfrac{y-4}{y}-\dfrac{3z+6}{z}&=1-\dfrac{2}{x}+1-\dfrac{4}{y}-3-\dfrac{6}{z}\
&=1+1-3-\dfrac{2}{x}-\dfrac{4}{y}-\dfrac{6}{z}\
&=-1-2\left(\dfrac{1}{x}+\dfrac{2}{y}+\dfrac{3}{z}\right)\
&=-1-2\cdot7\
&=-1-14\
&=-15
\end{align*}
$$

[magic axle]

catman
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[misty tusk]

@vernal flare

[vernal flare]

Oh ok I understand perfectly now

Thank you for helping me

[misty tusk]

np!

[vernal flare]

I hope you dont mind me asking but with questions similar to this one, how can I prepare myself to solve them?

Like what sub-subjects do I need to know

[misty tusk]

I would work on simplifying fractions with variables

[vernal flare]

Hm ok I will do some practice worksheets

Again thank you very much