Answer
$\displaystyle \frac{2}{1-2x}$
Work Step by Step
Simplifying Rational Expressions
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
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Numerator $:$ factor out 2...
$2(4x^{2}+2x+1)=$
... and, this is as far as it goes
(not a perfect square, can't find factors of 4 that add up to 2)
Denominator:
Numerator $:$ recognize a difference of cubes
$1^{3}-(2x)^{3}=(1-2x)(4x^{2}+2x+1)$
Expression = $\displaystyle \frac{2(4x^{2}+2x+1)}{(1-2x(4x^{2}+2x+1)}$
... divide both with the common factor: $(4x^{2}+2x+1)$
Expression = $\displaystyle \frac{2}{1-2x}$
