CPM Homework Help : INT3 Problem 11-42

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Home > INT3 > Chapter 11 > Lesson 11.1.4 > Problem 11-42

11-42.

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.

$\frac{7}{x+5}-\frac{4-6x}{x^2+10x+25}$
Step 1(d):
Begin by factoring the $2^{\text{nd}}$ denominator and then creating common denominators.
$\frac{x+5}{x + 5} \cdot \frac{7}{x+ 5} - \frac{4 - 6x}{(x+5)(x+5)}$
Step 2(d):
$\frac{7x+35}{(x+5)(x+5)} - \frac{4-6x}{(x+5)(x+5)}$
Step 3(d):
$\frac{(7x + 35 )-(4 - 6x)}{(x+5)(x+5)}$
Step 4(d):
Simplify the numerator.

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