  ### Home > AC > Chapter 11 > Lesson 11.1.2 > Problem11-25

11-25.

Use your method for multiplying and dividing fractions to simplify the expressions below.

1. $\frac{x+2}{x-1}\cdot\frac{x-1}{x-6}$

Multiply and look for factors that make $1$.

1. $\frac{(4x-3)(x+2)}{(x-5)(x-3)}\div\frac{(x-1)(x+2)}{(x-1)(x-3)}$

Dividing by a fraction is the
same as multiplying by its reciprocal.

Multiply the fractions and look for factors that make one.

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

$\frac{(4x-3)}{(x-5)}$

1. $\frac{(x-6)^2}{(2x+1)(x-6)}\cdot\frac{x(2x+1)(x+7)}{(x-1)(x+7)}$

See part (b).

$\frac{x(x-6)}{x-1}$

1. $\frac{(x+3)(2x-5)}{(3x-4)(x-7)}\div\frac{(2x-5)}{(3x-4)}$

See part (b).

1. $\frac{3x-1}{x+4}+\frac{x-5}{x+4}$

See part (b).

1. $\frac{x-3}{x+4}\cdot\frac{3x-10}{x+11}\cdot\frac{x+4}{3x-10}$

See part (b).

$\frac{x-3}{x+11}$