### Home > AC > Chapter 12 > Lesson 12.2.2 > Problem12-49

12-49.

Add, subtract, multiply, or divide the expressions below. Leave your answer as simplified as possible.

1. $\frac { 4 x ^ { 2 } - 13 x + 3 } { 5 x ^ { 2 } + 23 x - 10 } \cdot \frac { 5 x - 2 } { x ^ { 2 } + 6 x - 27 } \cdot \frac { x ^ { 2 } + 5 x - 36 } { 4 x - 1 }$

1. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 6 x + 9 } \div \frac { x ^ { 2 } - x - 6 } { x ^ { 2 } + 4 }$

1. $6 + \frac { 3 } { x + 1 }$

1. $\frac { 5 } { x } - \frac { 10 } { x ^ { 2 } + 2 x }$

$\frac { ( 4 x - 1 ) ( x - 3 ) } { ( 5 x - 1 ) ( x + 5 ) } \cdot \frac { ( 5 x - 2 ) } { ( x + 9 ) ( x - 3 ) } \cdot \frac { ( x + 9 ) ( x - 4 ) } { ( 4 x - 1 ) }$

$\frac { ( 4 x - 1 ) ( x - 3 ) ( 5 x - 2 ) ( x + 9 ) ( x - 4 ) } { ( 5 x - 2 ) ( x + 5 ) ( x + 9 ) ( x - 3 ) ( 4 x - 1 ) }$

Look for 1s.

$\frac { x - 4 } { x + 5 }$

$\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 6 x + 9 } \cdot \frac { x ^ { 2 } + 4 } { x ^ { 2 } - x - 6 }$

$6 \text { by } \frac { x + 1 } { x + 1 }$

$\frac { 6 ( x + 1 ) } { x + 1 } + \frac { 3 } { x + 1 }$

$\frac { 6 x + 9 } { x + 1 }$

Factor the denominator of the term on the right to help you find a common denominator.