Solve Rational Equations: example 8.70

Solve $\frac{1}{c} + \frac{1}{m} = 1 for c .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $\frac{1}{a} + \frac{1}{b} = c$ for $a .$

How did it go?


Note any value of the variable that would make any denominator zero.
Clear the fractions by multiplying both sides of the equations by the LCD, $c m$ .
Distribute.
Simplify.
Collect the terms with c to the right.
Factor the expression on the right.
To isolate c, divide both sides by $m - 1$ .
Simplify by removing common factors.