## DeadShot 2 years ago 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 ?

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

2. SheldonEinstein

3. SheldonEinstein

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.

4. SheldonEinstein

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.

5. SheldonEinstein

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!

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

7. SheldonEinstein

Yeah!