Add and Subtract Rational Expressions with Unlike Denominators: example 8.43

Add: $\frac{2 a}{2 a b + b^{2}} + \frac{3 a}{4 a^{2} - b^{2}} .$

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.

Add: $\frac{5 x}{x y - y^{2}} + \frac{2 x}{x^{2} + y^{2}} .$

How did it go?


Do the expressions have a common denominator? No. Rewrite each expression with the LCD.
Find the LCD.
Rewrite each rational expression as an equivalent rational expression with the LCD.
Simplify the numerators.
Add the rational expressions.
Simplify the numerator.
Factor the numerator.
There are no factors common to the numerator and denominator. The fraction cannot be simplified.


Do the expressions have a common denominator? No. Rewrite each expression with the LCD.
Find the LCD.
Rewrite each rational expression as an equivalent rational expression with the LCD.
Simplify the numerators.
Add the rational expressions.
Simplify the numerator.
Factor the numerator.
There are no factors common to the numerator and denominator. The fraction cannot be simplified.