Question

How do you multiply and simplify `\frac { x - 3} { x ^ { 2} + x - 2} \cdot \frac { 3x + 6} { x + 3}`?

Answer 1

`(3x^2-3x-18)/(x^3+4x^2+x-6)`

Explanation:

`((x-3)(3x+6))/((x^2+x-2)(x+3))`

= `(3x^2+6x-9x-18)/(x^3+3x^2+x^2+3x-2x-6)`

=`(3x^2-3x-18)/(x^3+4x^2+x-6)`

(Multiply out brackets using F.O.I.L method)
First ("first" terms of each binomial are multiplied together)
Outer ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second)
Inner ("inside" terms are multiplied—second term of the first binomial and first term of the second)
Last ("last" terms of each binomial are multiplied)

(^ from Wikipedia)