Solving an expression

[charred hill]

I got confused with the attached solution

My answer is 4 after multiplying the whole expression by 2:

4 + 2 - 2 + 2 x square root 2 - square root 2 - square root 2 = 4

How did it get 2 as the final answer?

[gusty spear]

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[steel herald]

Why did u multiply the expression by 2

To get rid of the fractions ?

That changes the expression

If you want to multiply by 2 then you need to cancel that change by dividing by 2

So in the end your answer is 4/2 = 2 and done

[manic ermine]

why multiply by 2? That's gonna end up giving you 4 and not 2

[charred hill]

Yes

[charred hill]

What do you mean?

If I want to get rid of the fraction, I have to divide all expression by 2?

[stable valve]

what's the original qn

[charred hill]

2 + (2^1/2) + 1/ (2 + 2^1/2) + 1/(2^1/2 -2)

[toxic sequoia]

Try working with the third and fourth terms separately first.

[charred hill]

Um I am a bit confused

[charred hill]

Sure

[charred hill]

Should I just multiply the fraction, instead of the whole expression, if I want to change the same denominator?

[toxic sequoia]

Of course.

[steel herald]

Because you can’t just multiply it by 2

Kind of like just randomly adding 1 to your answer

Like, it’s not allowed

[stable valve]

$2+\sqrt{2}+\frac{1}{2+\sqrt{2}}+\frac{1}{\sqrt{2}-2}$?

[muted fulcrum]

ooaa

[stable valve]

i mean, you should probably divide back by 2 since you did an operation

inverse of multiplication is division

[stable valve]

eh

you can if you know what you're doing

[stable valve]

hence

[steel herald]

Only if you divide by 2 after

Oh u said that nvm

But that’s the point , they don’t understand that

[dry lodge]

@charred hill

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