Question

Catalina and Yong Chan are simplifying $\frac{x}{a}-\frac{x}{b}$. Who is correct? Explain your reasoning.

Short answer

Since the result matches with Catalina and it doesn’t match with Yong Chan. Hence, Catalina is correct in solving the expression.

Step-by-step solution

Step 1. Write down the given expression.

The given equation is $\frac{x}{a}-\frac{x}{b}$ which is solved by both Catalina and Yong Chan as shown below.

Step 2. Simplify the equation.

The given equation $\frac{x}{a}-\frac{x}{b}$is solved as:

$\begin{array}{l}\frac{x}{a}-\frac{x}{b}=\frac{bx}{ab}-\frac{ax}{ab}\\ =\frac{bx-ax}{ab}\end{array}$

Since the result matches with Catalina and it doesn’t match with Yong Chan. Hence, Catalina is correct in solving the expression.

Step 3. Conclusion.

Since the result matches with Catalina and it doesn’t match with Yong Chan. Hence, Catalina is correct in solving the expression.