CPM Homework Help : AC Problem 10-105

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10-105.

Use your understanding of the number $1$ to simplify the rational expressions below.

$\frac{\left(x-3\right)\left(2x+9\right)\left(4x-3\right)}{\left(2x+9\right)\left(5x+1\right)\left(x-3\right)}$
Hint (a):
Simplify by finding factors that make 'one'.
$\frac{\left(x-3\right)\left(2x+9\right)\left(4x-3\right)}{\left(2x+9\right)\left(5x+1\right)\left(x-3\right)}$

$\frac{25x^2+20x+4}{25x^2-4}$
Hint (b):
Factor the expression, then use the same method as in part (a) to solve.
$\frac{\left(5x+2\right)\left(5x+2\right)}{\left(5x-2\right)\left(5x+2\right)}$

$\frac{16x^2+24x+8}{2x^2-2x-4}$
Hint (c):
Factor the expression, then use the same method as part (a).
Answer (c):
$\frac{4\left(2x+1\right)}{\left(x-2\right)}$

$\frac { 24 x y ^ { 2 } } { 36 x ^ { 2 } y }$
Hint (d):
Find common factors of the numerator and the denominator that make 'one'.
Answer (d):
$\frac{24xy^2}{36x^2y}=\frac{12}{12}\cdot\frac{2}{3}\cdot\frac{x}{x}\cdot\frac{1}{x}\cdot\frac{y}{y}\cdot\frac{y}{1}=\frac{2y}{3x}$

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