Answer:
Simplest form is [tex]\frac{(x+9)}{(x+4)}[/tex].
Step-by-step explanation:
Given : [tex]\frac{x^{2}+5x-36 }{x^{2}-16 }[/tex].
To find : What is its simplest form .
Solution : We have given that [tex]\frac{x^{2}+5x-36 }{x^{2}-16 }[/tex].
On factoring the numerator of given fraction we get,
[tex]x^{2} -4x+9x-36[/tex].
Taking common x (x -4) +9(x-4).
On grouping (x+9) (x-4) .
Now , Factoring the denominator of given fraction [tex]x^{2} -16[/tex] by [tex]a^{2} -b^{2} = (a-b)(a+b)[/tex]
(x-4) (x+4).
On substituting the numerator and denominator in given fraction we get,
[tex]\frac{(x+9)(x-4)}{(x-4)(x+4)}[/tex].
On simpification we get [tex]\frac{(x+9)}{(x+4)}[/tex].
Therefore , Simplest form is [tex]\frac{(x+9)}{(x+4)}[/tex].
