Question

Simplify.
X² -16 divide X²-3x-4

Answer 1

`((x+4))/((x+1))`

Explanation:

`(x^(2)-16)/(x^(2) -3x-4)`

The numerator (upper half) can be squared:

knowing
`x^(2)` = x ×x

and knowing 16 = 4×4

we can simplify the numerator to:

`((x+4)(x-4))/(x^(2) -3x-4)`

Taking a look at the bottom:

`x^(2) -3x-4`

We can say:

a = 1

b = -3

c = -4

So we need two number than sum to -3 and multiply to -4:

-4 + 1 = -3

-4 * 1 = -4

The two numbers are -4 and 1 so:

(x - 4)(x + 1)

insert into equation:

`((x+4)(x-4))/((x-4)(x+1))`

We can remove (x-4) from top and bottom to get:

`((x+4))/((x+1))`