Question

What is the simplified form of x minus 2 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x plus 4 ?

Answer 1

`(1)/((x+3)(x+1))`

Explanation:

given
`(x-2)/(x^2+x-6)` ÷
`(x^2+5x+4)/(x+4)`

factor the quadratic expressions in both fractions

x² + x - 6 = (x + 3)(x - 2) and x² + 5x + 4 = (x + 4)(x + 1)

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

=
`(x-2)/((x-2)(x+3))` ×
`(x+4)/((x+4)(x+1))`

In the first fraction (x - 2) cancels and in the second fraction (x + 4) cancels, leaving

`(1)/((x+3)(x+1))`