CPM Homework Help : AC Problem 12-5

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Home > AC > Chapter Ch12 > Lesson 12.1.1 > Problem 12-5

12-5.

Use your factoring shortcuts to simplify the following expressions.

$\frac{x^2-9}{x^2-6x+9}$
Step 1 (a):
$\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-3\right)}$
Step 2 (a):
$\frac{\left(x-3\right)}{\left(x-3\right)}=1$
Answer (a):
$\frac{\left(x+3\right)}{\left(x-3\right)}$

$\frac{2x+5}{4x^2-25}\cdot\frac{2x-5}{x+7}$
Step 1 (b):
$\frac{2x+5}{\left(2x+5\right)\left(2x-5\right)}\cdot\frac{2x-5}{x+7}$
Step 2 (b):
$\frac{\left(2x+5\right)\left(2x-5\right)}{\left(2x+5\right)\left(2x-5\right)\left(x+7\right)}$
Hint (b):
Look for ones.

Hint (c) and (d):

See part (b).

$\frac{x^2+x-20}{x^2-16}\cdot\frac{x^2+9x+20}{x^2+10x+25}$

$\frac{x^2+12x+36}{x^2-25}\div\frac{x+6}{x+5}$

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