Question

divide and simplify.
\\(\frac{3x}{8} \div \frac{9x + 18}{8x + 16}\\)
\\(\frac{3x}{8} \div \frac{9x + 18}{8x + 16} = \square\\)

Explanation:

Step1: Rewrite division as multiplication

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, $\frac{3x}{8} \div \frac{9x + 18}{8x + 16}$ becomes $\frac{3x}{8} \times \frac{8x + 16}{9x + 18}$.

Step2: Factor numerators and denominators

Factor the expressions: $8x + 16 = 8(x + 2)$ and $9x + 18 = 9(x + 2)$. Substitute these into the equation: $\frac{3x}{8} \times \frac{8(x + 2)}{9(x + 2)}$.

Step3: Cancel common factors

Cancel out the common factors: 8 in the numerator and denominator, and $(x + 2)$ in the numerator and denominator. We are left with $\frac{3x}{1} \times \frac{1}{9}$.

Step4: Multiply the fractions

Multiply the numerators and denominators: $\frac{3x \times 1}{1 \times 9} = \frac{3x}{9}$.

Step5: Simplify the fraction

Simplify $\frac{3x}{9}$ by dividing numerator and denominator by 3: $\frac{x}{3}$.

Answer:

$\frac{x}{3}$