Add and Subtract Rational Expressions with a Common Denominator: example 8.37

Subtract: $\frac{m^{2} - 6 m}{m^{2} - 1} - \frac{3 m + 2}{1 - m^{2}} .$

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.

Subtract: $\frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 y - 6}{4 - y^{2}} .$

How did it go?


The denominators are opposites, so multiply the second fraction by $\frac{−1}{−1}$ .
Simplify the second fraction.
The denominators are the same. Subtract the numerators.
Distribute.	$\frac{m^{2} - 6 m + 3 m + 2}{m^{2} - 1}$
Combine like terms.
Factor the numerator and denominator.
Simplify by removing common factors.
Simplify.


The denominators are opposites, so multiply the second fraction by $\frac{−1}{−1}$ .
Simplify the second fraction.
The denominators are the same. Subtract the numerators.
Distribute.	$\frac{m^{2} - 6 m + 3 m + 2}{m^{2} - 1}$
Combine like terms.
Factor the numerator and denominator.
Simplify by removing common factors.
Simplify.