Solve the equation for the indicated variable.
-$\frac { 1 } { a } + \frac { 1 } { b } = c \quad$ for $a$
A) $a = b c - \frac { 1 } { b }$
B) $a = \frac { 1 } { c } - b$
C) $a = \frac { 1 } { b c }$
D) $a = \frac { b } { b c - 1 }$

Question

Quizplus · Accepted Answer

To solve for $a$, start with the given equation: $\frac{1}{a} + \frac{1}{b} = c$. Isolate $\frac{1}{a}$ by subtracting $\frac{1}{b}$ from both sides: $\frac{1}{a} = c - \frac{1}{b}$. To find $a$, take the reciprocal of both sides, but first express the right side under a common denominator: $c - \frac{1}{b} = \frac{bc}{b} - \frac{1}{b} = \frac{bc - 1}{b}$. Thus, $a = \frac{b}{bc - 1}$.

Solve the Equation for the Indicated Variable 1a+1b=c\frac { 1 } { a } + \frac { 1 } { b } = c \quada1​+b1​=c

Solve the Equation for the Indicated Variable $\frac { 1 } { a } + \frac { 1 } { b } = c \quad$