Question

simplify.
\frac{\frac{x + 5}{12x^{3}}}{\frac{x + 5}{3x^{4}}}

Explanation:

Step1: Recall division of fractions rule

Dividing by a fraction is multiplying by its reciprocal. So $\frac{\frac{x + 5}{12x^{3}}}{\frac{x + 5}{3x^{4}}}=\frac{x + 5}{12x^{3}}\times\frac{3x^{4}}{x + 5}$.

Step2: Cancel out common factors

Cancel out the common factor $(x + 5)$ in the numerator and denominator. We get $\frac{1}{12x^{3}}\times\frac{3x^{4}}{1}$.

Step3: Multiply the remaining terms

Multiply the coefficients and the variables separately. $\frac{3x^{4}}{12x^{3}}=\frac{3}{12}\times\frac{x^{4}}{x^{3}}$.

Step4: Simplify the coefficient and the variable - part

Simplify $\frac{3}{12}=\frac{1}{4}$ and $\frac{x^{4}}{x^{3}}=x$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$). So $\frac{1}{4}\times x=\frac{x}{4}$.

Answer:

$\frac{x}{4}$