Question

May someone help me with this factor equation?

Answer 1

`(x^2+8x+9)/((x+3)(x-1))`

Explanation:

`(2x)/(x^2+2x-3)` +
`(x+3)/(x-1)` ← factor the denominator of first fraction

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

Before adding we require the denominators to be the same

Multiply numerator/denominator of second fraction by (x + 3)

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

Add the numerators leaving the common denominator ( LCD = (x + 3)(x - 1) )

=
`(2x+(x+3)(x+3))/((x+3)(x-1))` ← expand factors on numerator using FOIL

=
`(2x+x^2+6x+9)/((x+3)(x-1))`

=
`(x^2+8x+9)/((x+3)(x-1))`