CPM Homework Help : PC3 Problem 8-41

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8-41.

Simplify each of the following rational expressions.

$\frac { 4 x ^ { 2 } - 8 x } { x ^ { 2 } - 9 } \cdot \frac { x ^ { 2 } - x - 12 } { 2 x ^ { 3 } - 8 x ^ { 2 } }$
Hint (a):
Factor all of the expressions. Then simplify.
Step (a):
$\frac{4x(x-2)}{(x-3)(x+3)}\cdot \frac{(x-4)(x+3)}{2x^2(x-4)}$

$(x^2-y^2)\div\frac{x^2+2xy+y^2}{4x^2+4xy}$
Hint (b):
Write $\left(x^{2} − y^{2}\right)$ over $1$ . Then follow the same process as shown in part (a).

$\frac { 6 x ^ { 4 } - 16 x ^ { 3 } - x ^ { 2 } + 14 x + 3 } { 2 x ^ { 2 } - 4 x - 1 }$
Hint (c):
Use long division.

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