## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\frac{ab}{b+a}$ = t
Problem: $\frac{1}{t}$ = $\frac{1}{a}$ + $\frac{1}{b}$ 1. Multiplying both sides by the least common multiple (LCM) of the denominators: $(tab) \frac{1}{t}$ = $\frac{1}{a} (tab)$ + $\frac{1}{b}(tab)$ 2. Simplify by removing factors (t is cancelled out in $\frac{1}{t}$, a is cancelled out in $\frac{1}{a}$, and b is cancelled out in $\frac{1}{b}$.) This leaves you with ab = tb + ta 3. Factor out t on the right side ab = t (b+a) 4. Divide both sides by b+a $\frac{ab}{b+a}$ = $\frac{t(b+a)}{b+a}$ 5. Answer: $\frac{ab}{b+a}$ = t