Add and Subtract Rational Expressions with Unlike Denominators · Exercise 85

Felipe thinks $\frac{1}{x}+\frac{1}{y}$ is $\frac{2}{x+y}.$

ⓐ Choose numerical values for x and y and evaluate $\frac{1}{x}+\frac{1}{y}.$
ⓑ Evaluate $\frac{2}{x+y}$ for the same values of x and y you used in part (a).
ⓒ Explain why Felipe is wrong.
ⓓ Find the correct expression for $\frac{1}{x}+\frac{1}{y}.$

This is an open-ended exercise: its source gives no single answer.

OpenStax, Elementary Algebra 2e · §8.4 Add and Subtract Rational Expressions with Unlike Denominators · Exercise 85