CPM Homework Help : AC Problem 11-25

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11-25.

Use your method for multiplying and dividing fractions to simplify the expressions below.

$\frac{x+2}{x-1}\cdot\frac{x-1}{x-6}$
Hint (a):
Multiply and look for factors that make $1$ .

$\frac{(4x-3)(x+2)}{(x-5)(x-3)}\div\frac{(x-1)(x+2)}{(x-1)(x-3)}$
Hint 1(b):
Dividing by a fraction is the
same as multiplying by its reciprocal.
Hint 2(b):
Multiply the fractions and look for factors that make one.
$\frac{\left(4x-3\right) \cancel{\left(x+2\right)} \cancel{\left(x-1\right)} \cancel{\left(x-3\right)}} {\left(x-5\right) \cancel{\left(x+2\right)} \cancel{\left(x-1\right)} \cancel{\left(x-3\right)}}$
Answer (b):
$\frac{(4x-3)}{(x-5)}$

$\frac{(x-6)^2}{(2x+1)(x-6)}\cdot\frac{x(2x+1)(x+7)}{(x-1)(x+7)}$
Hint (c):
See part (b).
Answer (c):
$\frac{x(x-6)}{x-1}$

$\frac{(x+3)(2x-5)}{(3x-4)(x-7)}\div\frac{(2x-5)}{(3x-4)}$
Hint (d):
See part (b).

$\frac{3x-1}{x+4}+\frac{x-5}{x+4}$
Hint (e):
See part (b).

$\frac{x-3}{x+4}\cdot\frac{3x-10}{x+11}\cdot\frac{x+4}{3x-10}$
Hint (f):
See part (b).
Answer (f):
$\frac{x-3}{x+11}$

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