Chapter 6.7, Problem 8E

To determine

To simplify: the expression $\frac{\frac{3}{x}}{\frac{1}{x}-\frac{1}{3x}}$.

Answer to Problem 8E

  $\frac{9}{2}$.

Explanation of Solution

Given information:

  $\frac{\frac{3}{x}}{\frac{1}{x}-\frac{1}{3x}}$

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 ,

  $\frac{\frac{3}{x}}{\frac{1}{x}-\frac{1}{3x}}$

Now,

  $\text{Least Common Denominator = }3x$

Multiplying by LCD we get,

  $\begin{array}{l}=\frac{\left(\frac{3}{x}\right)3x}{\left(\frac{1}{x}-\frac{1}{3x}\right)3x}\\ =\frac{9}{3-1}\\ =\frac{9}{2}\end{array}$

Thus, the solution is $\frac{9}{2}$ .