Chapter 11.5, Problem 7LC

To determine

The error in the work shown in the given calculation.

Answer to Problem 7LC

  $\text{Error in taking LCD}$

Explanation of Solution

Given:

The calculation,

  

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
1. Multiply both sides of equations by LCD(least common denominator) of all denominators.
2. Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In the given calculation, student did mistake in second step while taking the LCD. Observe that 1 is a whole number while 1/m is a fraction, so it must added by taking the LCD as shown below

  $\begin{array}{c}1+\frac{1}{m}=\frac{1}{5}\\ \frac{1}{1}\cdot \frac{m}{m}+\frac{1}{m}=\frac{1}{5}\\ \frac{m}{m}+\frac{1}{m}=\frac{1}{5}\\ \frac{m+1}{m}=\frac{1}{5}\end{array}$ .

Then simplify further by cross multiplying as shown below,

  $\begin{array}{c}1+\frac{1}{m}=\frac{1}{5}\\ \frac{m+1}{m}=\frac{1}{5}\\ 5\left(m+1\right)=m\cdot 1\\ 5m+5=m\\ 5m+5-m=m-m\\ 4m+5=0\\ 4m=-5\\ m=\frac{-5}{4}\end{array}$

Thus, the student did mistake in taking LCD in second step.