  ### Home > CCA2 > Chapter 3 > Lesson 3.2.4 > Problem3-107

3-107.

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

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

Look for Giant Ones. Does anything factor out?

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

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

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

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

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

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

$4x−12$ can be factored, too.

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