Simplify the complex fraction.
-$\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { c }$ for $c$
A) $c = \frac { a + b } { a b }$
B) $c = a + b$
C) $c = a b ( a + b )$
D) $c = \frac { a b } { a + b }$

Question

Quizplus · Accepted Answer

We can first find a common denominator for the left side of the equation: $\frac{1}{a} + \frac{1}{b} = \frac{b}{ab} + \frac{a}{ab} = \frac{a+b}{ab}$. Setting this equal to the right side, we get $\frac{a+b}{ab} = \frac{1}{c}$. Multiplying both sides by $\frac{ab}{a+b}$, we find that $c = \frac{ab}{a+b}$. Therefore, the answer is choice D.

Simplify the Complex Fraction 1a+1b=1c\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { c }a1​+b1​=c1​

Simplify the Complex Fraction $\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { c }$