Add and Subtract Rational Expressions with Unlike Denominators: example 8.49

Simplify: $\frac{2 u}{u - 1} + \frac{1}{u} - \frac{2 u - 1}{u^{2} - u} .$

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.

Simplify: $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1} .$

How did it go?


Do the rational expressions have a common denominator? No.
Find the LCD.
Rewrite each rational expression as an equivalent rational expression with the LCD.

Write as one rational expression.
Simplify.
Factor the numerator, and remove common factors.
Simplify.


Do the rational expressions have a common denominator? No.
Find the LCD.
Rewrite each rational expression as an equivalent rational expression with the LCD.

Write as one rational expression.
Simplify.
Factor the numerator, and remove common factors.
Simplify.