Question

simplify.
\frac{\frac{4x + 16}{x^2}}{\frac{12x + 36}{x}}

Explanation:

Step1: Rewrite as division

The complex fraction can be rewritten as $\frac{4x + 16}{x^2} \div \frac{12x + 36}{x}$.

Step2: Invert and multiply

Dividing by a fraction is multiplying by its reciprocal, so we get $\frac{4x + 16}{x^2} \times \frac{x}{12x + 36}$.

Step3: Factor numerators/denominators

Factor out 4 from $4x + 16$: $4(x + 4)$; factor out 12 from $12x + 36$: $12(x + 3)$. Now the expression is $\frac{4(x + 4)}{x^2} \times \frac{x}{12(x + 3)}$.

Step4: Cancel common factors

Cancel $x$ (since $x^2 = x \times x$ and we have one $x$ in the numerator) and simplify 4/12 to 1/3. We get $\frac{4(x + 4) \times x}{x^2 \times 12(x + 3)} = \frac{(x + 4)}{3x(x + 3)}$.

Answer:

$\frac{x + 4}{3x(x + 3)}$