### Home > AC > Chapter 10 > Lesson 10.1.3 > Problem10-30

10-30.

Multiply or divide the expressions below. Leave your answers as simplified as possible.

1. $\frac{\left(3x-1\right)\left(x+7\right)}{4\left(2x-5\right)}\cdot\frac{10\left(2x-5\right)}{\left(4x+1\right)\left(x+7\right)}$

Look for Giant Ones. Does anything factor out?

Remember, $10$ and $4$ have a common factor, too.

$\frac{5\left(3x-1\right)}{2\left(4x+1\right)}$

1. $\frac{\left(m-3\right)\left(m+11\right)}{\left(2m+5\right)\left(m-3\right)}\div\frac{\left(4m-3\right)\left(m+11\right)}{\left(4m-3\right)\left(2m+5\right)}$

Take the reciprocal of the divisor (the fraction on the right), and multiply the resulting fractions. Does anything factor out before you begin multiplying?

$1$

1. $\frac{2p^2+5p-12}{2p^2-5p+3}\cdot\frac{p^2+8p-9}{3p^2+10p-8}$

Refer to part (a). Factor each of the trinomials first. (Use a generic rectangle.)

1. $\frac{4x-12}{x^2+3x-10}\div\frac{2x^2-13x+21}{2x^2+3x-35}$

$4x-12$ can be factored, too.

$\frac{4}{x-2}$