CPM Homework Help : INT3 Problem 11-109

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11-109.

For each of the following rational expressions, add or subtract, then simplify.

$\frac { 2 - x } { x + 4 } + \frac { 3 x + 6 } { x + 4 }$
Step 1(a):
The denominators are the same, so just add the numerators.
$\frac{ 2x+8 }{x+4 }$
Step 2(a):
Factor the numerator and look for a Giant One.
Answer (a):
$2$

$\frac { 3 } { ( x + 2 ) ( x + 3 ) } + \frac { x } { ( x + 2 ) ( x + 3 ) }$
Hint (b):
See part (a).

$\frac { 3 } { x - 1 } - \frac { 2 } { x - 2 }$
Step 1(c):
The product of the two denominators is the common denominator. Multiply each term by a Giant One to make the denominators the same.
$\left( \frac{x-2}{x-2} \right) \cdot \left( \frac{3}{x-1}\right) -\left( \frac{2}{x-2}\right)·\left( \frac{x-1}{x-1}\right)$
Step 2(c):
Distribute:
$\frac{(3x-6)}{(x-2)(x-1)}-\frac{(2x -2)}{(x-2)(x-1)}$
Step 3(c):
Now, subtract. Notice you are subtracting a negative $2$ in the second term.
Answer (c):
$\frac{x-4}{(x-2)(x-1)}$

$\frac { 8 } { x } - \frac { 4 } { x + 2 }$
Hint (d):
See part (c).

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