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

Simplest form is
`((x+9))/((x+4))`.

Explanation:

Given :
`(x^(2)+5x-36 )/(x^(2)-16 )`.

To find : What is its simplest form .

Solution : We have given that
`(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,

`((x+9)(x-4))/((x-4)(x+4))`.

On simpification we get
`((x+9))/((x+4))`.

Therefore , Simplest form is
`((x+9))/((x+4))`.