CPM Homework Help : AC Problem 11-13

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Home > AC > Chapter Ch11 > Lesson 11.1.1 > Problem 11-13

11-13.

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

$\frac{12x^2+4x-1}{36x^2-12x+1}\cdot\frac{x^2-64}{2x^2+17x+8}$
Hint 1(a):
Factor the expressions, then multiply them.
$\frac{\left(2x+1\right)\left(6x+1\right)}{(6x-1)(6x-1)}\cdot\frac{\left(x-8\right)\left(x+8\right)}{(2x+1)(x+8)}$
$\frac{\left(2x+1\right)\left(6x+1\right)\left(x-8\right)\left(x+8\right)}{\left(6x-1\right)\left(6x-1\right)\left(2x+1\right)\left(x+8\right)}$
Hint 2(a):
Look for factors that make $1$ .
$\frac{\cancel{\left(2x+1\right)} \left(6x+1\right) \left(x-8\right) \cancel{\left(x+8\right)}} {\left(6x-1\right) \left(6x-1\right) \cancel{\left(2x+1\right)} \cancel{\left(x+8\right)}}$
Answer (a):
$\frac{(x-8)}{(6x-1)}$

$\frac{2x^2-10x}{x^2-4}\div\frac{x^2-5x}{x^2-4x-12}$
Hint (b):
Change division to multiplication, then see part (a).

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