Question

What is the quotient of the equation Below in simplest form? State any restrictions on the variable

Answer 1

A

Explanation:

Factor the numerators/ denominators where possible, that is

`(-(x-5))/((x+4)(x-1))` ÷
`((x-5)(x+3))/((x+4)(x+1))`

Leave the first fraction, change division to multiplication and turn the second fraction upside down.

=
`(-(x-5))/((x+4)(x-1))` ×
`((x+4)(x+1))/((x-5)(x+3))`

Cancel the factors (x - 5) and (x + 4) from numerator/denominator

=
`(-1)/((x-1))` ×
`((x+1))/((x+3))`

=
`(-(x+1))/((x-1)(x+3))` , x ≠ 1, x ≠ - 3