Question

simplify the complex rational expression.

\\\frac{7}{\frac{5}{x+5}+3}\\

\\\frac{7}{\frac{5}{x+5}+3} = \boxed{\quad}\\

(simplify your answer. type your answer in factored form. use integers or fractions for any numbers in the expression.)

Explanation:

Simplify the denominator

Using the Rational Expressions knowledge point

$$ \frac{5}{x+5} + 3 = \frac{5 + 3(x+5)}{x+5} = \frac{5 + 3x + 15}{x+5} = \frac{3x + 20}{x+5} $$

Divide the numerator by the simplified denominator

Using the Rational Expressions knowledge point

$$ \frac{7}{\frac{3x+20}{x+5}} = 7 \cdot \frac{x+5}{3x+20} = \frac{7(x+5)}{3x+20} $$

Answer:

Simplify the complex rational expression.

$$\frac{7}{\frac{5}{x+5}+3} =$$

<blank>\(\frac{7(x+5)}{3x+20}\)</blank>