Question

Solve. 4 - x^2 over x^2 + 2x - 8.

Answer 1

Factor both of them

4 - x^2 and x^2 + 2x - 8.

Answer 2

Okay? Then what?

Answer 3

You'll be able to cancel out common terms

can you tell me what you got after factoring ?

4-x^2= ?
x^2+ 2x - 8 = ?

Answer 4

well, the common factor for 4 - x^2 is 2x, right?

Answer 5

@fallingangel No, 4 - x^2 is prime.

Answer 6

Oh... See? I need help. :/

Answer 7

No factor it ..
4-x^2 can be written as (2)^2 -(x)^2

\[a^2-b^2=(a+b)(a-b)\]

Answer 8

\[(2)^2-(x)^2=(2-x)(2+x)\]

Answer 9

\(\Large \color{purple}{\rightarrow x^2 -2x + 4x - 8 }\)

\(\Large \color{purple}{\rightarrow x(x - 2) + 4(x - 2) }\)

\(\Large \color{purple}{\rightarrow (4 + x)(x - 2) }\)

^^ FACTORIZATION

Answer 10

\[\Large \frac{4-x^2}{x^2+2x-8}=\frac{(4+x)(4-x)}{(4+x)(x-2)}\]

Answer 11

Now you can cancel out 4+x

Answer 12

@fallingangel did you understnad ?

Answer 13

Thank you so much. :)

Answer 14

Yes, I do.

Answer 15

Now, just cross multiply the numerator of the first fraction and denominator of the other and vice-versa

Answer 16

@ParthKohli cross multiply ?

Answer 17

That's what I was wondering.

Answer 18

I mean, cross-multiply on both sides of the equation.

Answer 19

\(\Large \color{purple}{\rightarrow {a \over b} = {c \over d} \rightarrow ad = bc }\)

Answer 20

That's what I meant.

Answer 21

Where would I have used that though?

Answer 22

@ParthKohli you probably got the question wrong

Answer 23

No wait, I thought it was an equation from one of your replies :P