Chapter 11.6, Problem 73HP

To determine

To find: whether the expression is true or false

Answer to Problem 73HP

Here, the expression is always true.

Explanation of Solution

Given:

  $\frac{a}{x}+\frac{b}{y}=\frac{ay+bx}{xy};x\ne 0,y\ne 0$

Calculation:

The expression is simplified below.

  $\frac{a}{x}+\frac{b}{y}$

  $=\frac{a}{x}\left(\frac{y}{y}\right)+\frac{b}{y}\left(\frac{x}{x}\right)$

  $=\frac{ay}{xy}+\frac{bx}{xy}$

  $=\frac{ay+bx}{xy}$

Here, the expression is always true.

Conclusion:

Therefore, the expression is always true.