Chapter 6.7, Problem 9E

To determine

To simplify: the expression $\frac{\frac{9c^2}{5d^4}}{\frac{3c^2}{10d^3}}$.

Answer to Problem 9E

  $\frac{6}{d}$.

Explanation of Solution

Given information:

  $\frac{\frac{9c^2}{5d^4}}{\frac{3c^2}{10d^3}}$

Formula used:

Method 1.

Simplify the numerator and denominator . Then express the fraction as quotient using the ÷ sign. Multiply by the reciprocal of the divisor.

Method 2.

Find the LCD of all simple fractions . Multiply the numerator and the denominator of the complex fraction by the LCD.

Calculation:

Consider ,

  $\frac{\frac{9c^2}{5d^4}}{\frac{3c^2}{10d^3}}$

Now,

  $=\frac{\frac{9c^2}{5d^4}}{\frac{3c^2}{10d^3}}=\frac{9c^2}{5d^4}÷\frac{3c^2}{10d^3}$

  $\begin{array}{l}=\frac{9c^2}{5d^4}\times \frac{10d^3}{3c^2}\\ =\frac{6}{d}\end{array}$

Thus, the solution is $\frac{6}{d}$.