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