Answer
$\frac{ab}{b+a}$ = t
Work Step by Step
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
