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

Multiply and look for factors that make 1.

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

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

Multiply the fractions and look for factors that make one. $\frac { ( 4 x - 3 ) } { ( x - 5 ) }$

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

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

See part (b).

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

See part (b).

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

See part (b).

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