### Home > A2C > Chapter 6 > Lesson 6.2.1 > Problem6-65

6-65.

Some of the following algebraic fractions have common denominators and some do not. Add or subtract the expressions and simplify, if possible.

1. $\frac { 3 } { ( x - 4 ) ( x + 1 ) } + \frac { 6 } { x + 1 }$

$\frac{3}{(x-4)(x+1)}+\frac{6}{x+1}\cdot \frac{x-4}{x-4}$

$\frac{3+6(x-4)}{(x-4)(x+1)}$

$\frac{6x-21}{(x-4)(x+1)}$

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

See part (a).

1. $\frac { x } { x ^ { 2 } - x - 2 } - \frac { 2 } { x ^ { 2 } - x - 2 }$

Try factoring after subtracting.

1. $\frac { x + 2 } { x ^ { 2 } - 9 } - \frac { 1 } { x + 3 }$

Factor to find the common denominator, then use the strategy from part (a) to simplify.

$\frac{5}{x^2-9}$

$\text{If your answer was }-\frac{1}{x²-9},$

check the step where you subtracted.

$−\left(x − 3\right) = x + 3$