Solve Rational Equations: example 8.59

Solve: $\frac{1}{x} + \frac{1}{3} = \frac{5}{6} .$

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.

Solution
$Step three is to clear the fractions by multiplying both sides of the equation by the LCD. Multiply both sides of the equation by the LCD, 6 x to get 6 times 1 divided by x plus one-third equals 6 x times five-sixths. Use the Distributive Property to get 6 x times 1 divided by x plus 6 x times one-third equals 6 x times five-sixths. Simplify – and notice, no more fractions and we have 6 plus 2 x equals 5 x.$

Your turn

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

Solve: $\frac{1}{y} + \frac{2}{3} = \frac{1}{5} .$

How did it go?