Solve Rational Equations: example 8.61

Solve: $\frac{5}{3 u - 2} = \frac{3}{2 u} .$

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: $\frac{1}{x - 1} = \frac{2}{3 x} .$

How did it go?


Note any value of the variable that would make any denominator zero.
Find the least common denominator of all denominators in the equation. The LCD is $2 u (3 u - 2)$ .
Clear the fractions by multiplying both sides of the equation by the LCD.
Remove common factors.
Simplify.
Multiply.
Solve the resulting equation.
We did not get 0 or $\frac{2}{3}$ as algebraic solutions.


Note any value of the variable that would make any denominator zero.
Find the least common denominator of all denominators in the equation. The LCD is $2 u (3 u - 2)$ .
Clear the fractions by multiplying both sides of the equation by the LCD.
Remove common factors.
Simplify.
Multiply.
Solve the resulting equation.
We did not get 0 or $\frac{2}{3}$ as algebraic solutions.