Answer:
[tex]c=\frac{ab}{a+b}[/tex]
Step-by-step explanation:
To solve for [tex]c[/tex], our goal is to isolate it.
Start by multiply both sides by [tex]ab[/tex]. That way, we'll still have only one term with [tex]c[/tex], but we'll be able to get rid of two messy fractions.
[tex]b+a=\frac{ab}{c}[/tex]
Taking the reciprocal of both sides:
[tex]\frac{1}{a+b}=\frac{c}{ab},\\c=\boxed{\frac{ab}{a+b}}[/tex]
*Note: You cannot take the reciprocal of both sides if you're adding fractions. This is why we can't just take the reciprocal of both sides in the initial equation.
Alternate solution:
[tex]\frac{1}{a}+\frac{1}{b}=\frac{b}{ab}+\frac{a}{ab}=\frac{1}{c},\\\\\frac{b+a}{ab}=\frac{1}{c},\\\\c=\frac{ab}{b+a}=\boxed{\frac{ab}{a+b}}[/tex]
