CPM Homework Help : AC Problem 12-25

Add, subtract, multiply, or divide the following rational expressions. Simplify your answers, if possible.

$\frac { 2 x } { 3 x ^ { 2 } + 16 x + 5 } + \frac { 10 } { 3 x ^ { 2 } + 16 x + 5 }$

$\frac { x ^ { 2 } - x - 12 } { 3 x ^ { 2 } - 11 x - 4 } \cdot \frac { 3 x ^ { 2 } - 20 x - 7 } { x ^ { 2 } - 9 }$

$\frac { 2 x ^ { 2 } + 8 x - 10 } { 2 x ^ { 2 } + 15 x + 25 } \div \frac { 4 x ^ { 2 } + 20 x - 24 } { 2 x ^ { 2 } + x - 10 }$

Hint (a):

Add the numerators and reduce. Factor and find any $1$ s.

Hint (b):

Factor the expressions.
Reduce by looking for factors in the numerator and denominator that make $1$ .

Answer (b):

$\frac { x - 7 } { x - 3 }$

Hint (c):

Factor each expression. Look for $1$ s.

Step (d):

$4 x ^ { 2 } + 5 x - 6 = ( x + 2 ) ( 4 x - 3 )$