Chapter SH, Problem 10OWRE

Solution

To simplify the expression $\frac{13}{2x}-\frac{13}{3x}$ .

  $\frac{13}{6x}$

Given:

The expression, $\frac{13}{2x}-\frac{13}{3x}$.

Concept Used:

To add or subtract fractions with unlike denominators, follow the below steps:

Step 1: Find the least common multiple (LCM) for the denominators.

Step 2: Multiply the numerator and denominator to get like denominators.

Step 3: Turn the other fractions into equivalent fractions.

Step 4: Add the numerators over the common denominator.

Step 5: Simplify and reduce the answer if necessary.

Calculation:

In order to simplify the given expression $\frac{13}{2x}-\frac{13}{3x}$ , note that least common multiple of 2x and 3x is 6x . So, make both the denominators equal to the LCM and combine the numerators directly over the common denominator as shown below

  $\begin{array}{c}\frac{13}{2x}-\frac{13}{3x}=\frac{13}{2x}\cdot \frac{3}{3}-\frac{13}{3x}\cdot \frac{2}{2}\\ =\frac{39}{6x}-\frac{26}{6x}\\ =\frac{39-26}{6x}\\ =\frac{13}{6x}\end{array}$

Thus, the simplified expression is $\frac{13}{6x}$ .