  ### Home > INT3 > Chapter 11 > Lesson 11.1.4 > Problem11-42

11-42.

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

These fractions have the same denominator.

After adding the fractions, factor to see if you can find any Giant Ones to remove.

$\frac{2}{3x+1}$

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

Factor each polynomial. Look for Giant Ones to remove.

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

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

Take the reciprocal of the divisor and factor each polynomial. Remove Giant Ones and multiply what's left.

1. $\frac { 7 } { x + 5 } - \frac { 4 - 6 x } { x ^ { 2 } + 10 x + 25 }$

Begin by factoring the $2^{\text{nd}}$ denominator and then creating common denominators.

$\frac{x+5}{x + 5} \cdot \frac{7}{x+ 5} - \frac{4 - 6x}{(x+5)(x+5)}$

$\frac{7x+35}{(x+5)(x+5)} - \frac{4-6x}{(x+5)(x+5)}$

$\frac{(7x + 35 )-(4 - 6x)}{(x+5)(x+5)}$

Simplify the numerator.