Question

What is the simplified form of x plus 3 over x squared minus x minus 12 • x minus 4 over x squared minus 8x plus 16 ?

Answer 1

\[\frac{ x+3 }{ x^2-x-12 }*\frac{ x-4 }{ x^2-8x+16 }\]

Answer 2

@DeadShot

Answer 3

First you need to factorize both denominators.

i would show you how to factorize the denominator, I would take \(x^2 - x -12\) as the example and then you have to proceed yourself.

Answer 4

I have \(x^2 - x - 12\)

\( x^2 + 3x - 4x -12\) = \(x(x+3) - 4(x+3)\)
\((x-4)(x+3)\)

This is how I factorized \(x^2-x-12\) by using "middle term splitting" method.

Similarly, factorize \(x^2 - 8x + 16\) by splitting -8x into -4x and -4x :
\(x^2 - 4x -4x + 16\)

and then do the proceedings.

Answer 5

You will have then : \(\cfrac{x+3}{(x-4)(x+3)} \times \cfrac{(x-4)}{x^2-8x+16}\)
\(\cfrac{(x+3)(x-4)}{(x-4)(x+3)(x^2-8x+16)}\)
\(\cfrac{\cancel{(x+3)(x-4)}}{\cancel{(x-4)(x+3)} (x^2-8x+16)}\)
\(\cfrac{1}{x^2-8x+16}\)

put the factorized form of \(x^2-8x+16\) on the place of it and you will get the required answer.

I hope it helped. Post here if you get any problem Do not forget to tell what you get..

best of luck!

Answer 6

I got \[\frac{ 1 }{ (x - 4)^2 }\]is that correct?

Answer 7

Yeah!