Question

What is the simplest form of x^2+5x-36/x^2-16

Answer 1

The answer is A. x+9/x+4

Answer 2

Answer:

Simplest form is $\frac{(x+9)}{(x+4)}$.

Step-by-step explanation:

Given : $\frac{x^{2}+5x-36 }{x^{2}-16 }$.

To find : What is its simplest form .

Solution : We have given that  $\frac{x^{2}+5x-36 }{x^{2}-16 }$.

On factoring the numerator of given fraction we get,

                    $x^{2} -4x+9x-36$.

Taking common  x (x -4) +9(x-4).

On grouping (x+9) (x-4) .

Now , Factoring the denominator of given fraction $x^{2} -16$ by $a^{2} -b^{2} = (a-b)(a+b)$

                  (x-4) (x+4).

On substituting the numerator and  denominator in given fraction we get,

$\frac{(x+9)(x-4)}{(x-4)(x+4)}$.

On simpification we get $\frac{(x+9)}{(x+4)}$.

Therefore , Simplest form is $\frac{(x+9)}{(x+4)}$.