Question

What is the simplest form of x^2+5X-36/x^2-16
X+9/X+4
9/4
X+9/X-4
-9/4

Answer 1

`\frac{ {x} + 9}{x - 4}`

Explanation:

`\frac{ {x}^(2) + 5x - 36}{ {x}^(2) - 16} \\ \\ = \frac{ {x}^(2) + 9x - 4x- 36}{ {x}^(2) - {(4)}^(2) } \\ \\ = \frac{ x({x} + 9) - 4(x + 9)}{ (x + 4)(x - 4) } \\ \\ = \frac{ ({x} + 9) \cancel{(x - 4)}}{ \cancel{(x + 4)}(x - 4) } \\ \\ = \frac{ {x} + 9}{x - 4}`