Chapter 11.1, Problem 43PPE

To determine

Describe and correct the error

Answer to Problem 43PPE

Simplified expression: $\frac{x^2+2x}{2x}=\frac{(x+2)}{2}$

Explanation of Solution

Given:

A student simplified a rational a rational expression as shown at the right. Describe and correct the error.

The figure:

Concept Used:

We can only cancel the factors, not a single term. First we need to factorize the expression and then cancel the common factor.

Calculation:

  $\frac{x^2+2x}{2x}=\frac{x(x+2)}{2·x}=\frac{(x+2)}{2}$

While simplifying the rational expression, we cannot cancel 2x from numerator and denominator without factoring the numerator.

Simplified expression: $\frac{x^2+2x}{2x}=\frac{(x+2)}{2}$

Thus, simplified expression: $\frac{x^2+2x}{2x}=\frac{(x+2)}{2}$