Question

PLEASE help me with this question! No nonsense answers please, and full solutions!

Answer 1

third option

Explanation:

Given

`(x+5)/(x-2)` +
`(x+6)/(x-4)`

Multiply the numerator/denominator of the first fraction by (x - 4)

Multiply the numerator/denominator of the second fraction by (x - 2)

=
`((x+5)(x-4))/((x-2)(x-4))` +
`((x+6)(x-2))/((x-2)(x-4))`

Express the 2 fractions over the common denominator

=
`((x+5)(x-4)+(x+6)(x-2))/((x-2)(x-4))` ← expand numerator/ denominator using FOIL

=
`(x^2+x-20+x^2+4x-12)/(x^2-6x+8)`

=
`(2x^2+5x-32)/(x^2-6x+8)`