Question

current objective
simplify a complex rational expression by wr

question
divide: \frac{2 - \frac{2}{u + 2}}{\frac{1}{u + 2} + \frac{u}{2}}

provide your answer below:

Explanation:

Simplify the numerator

Using the Complex Rational Expressions knowledge point

$$ 2 - \frac{2}{u+2} = \frac{2(u+2) - 2}{u+2} = \frac{2u + 4 - 2}{u+2} = \frac{2u + 2}{u+2} $$

Simplify the denominator

Using the Complex Rational Expressions knowledge point

$$ \frac{1}{u+2} + \frac{u}{2} = \frac{2(1) + u(u+2)}{2(u+2)} = \frac{2 + u^2 + 2u}{2(u+2)} = \frac{u^2 + 2u + 2}{2(u+2)} $$

Divide the simplified numerator by the simplified denominator

Using the Complex Rational Expressions knowledge point

$$ \frac{\frac{2u+2}{u+2}}{\frac{u^2+2u+2}{2(u+2)}} = \frac{2u+2}{u+2} \cdot \frac{2(u+2)}{u^2+2u+2} $$

Simplify the resulting expression

Using the Complex Rational Expressions knowledge point

$$ \frac{2(u+1)}{u+2} \cdot \frac{2(u+2)}{u^2+2u+2} = \frac{4(u+1)}{u^2+2u+2} = \frac{4u+4}{u^2+2u+2} $$

Answer:

Divide: <blank>\(\frac{4u+4}{u^2+2u+2}\)</blank>