CPM Homework Help : AC Problem 12-25

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Home > AC > Chapter Ch12 > Lesson 12.1.3 > Problem 12-25

12-25.

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

$\frac { 2 x } { 3 x ^ { 2 } + 16 x + 5 } + \frac { 10 } { 3 x ^ { 2 } + 16 x + 5 }$
Hint (a):
These fractions have the same denominator.
More Help (a):
After adding the fractions, factor to see if you can find any Giant Ones to remove.
Answer (a):
$\frac{2}{3x+1}$

$\frac{x^2-x-12}{3x^2-11x-4}\cdot\frac{3x^2-20x-7}{x^2-9}$
Hint (b):
Factor each polynomial. Look for Giant Ones to remove.
Answer (b):
$\frac{x-7}{x-3}$

$\frac{2x^2+8x-10}{2x^2+15x+25}\div\frac{4x^2+20x-24}{2x^2+x-10}$
Hint (c):
Take the reciprocal of the divisor and factor each polynomial. Remove Giant Ones and multiply what's left.

$\frac{16x-12}{4x^2+5x-6}-\frac{3}{x+2}$
Step (d):
This is the denominator.
$4x^2+5x-6=\left(x+2\right)\left(4x-3\right)$

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