Chapter 11.4, Problem 34PPE

To determine

What error did the student make?

Answer to Problem 34PPE

The error is that student add the denominators also

Explanation of Solution

Given:

Given equation

  

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 order to solve the equation $\frac{2}{x+3}+\frac{3}{x+3}$ , observe that the LCD of all the denominators is $8x$ . So simplify further as shown below

  $\begin{array}{c}\frac{2}{x+3}+\frac{3}{x+3}=\frac{2+3}{x+3}\\ =\frac{5}{x+3}\end{array}$

Thus, the solution of the given equation is $\frac{5}{x+3}$

The error is that student add the denominators also