Home > A2C > Chapter 7 > Lesson 7.3.5 > Problem7-225

7-225.

Add or subtract and simplify each of the following expressions. Justify that each step of your process makes sense.

1. $\frac { 3 x } { x ^ { 2 } + 2 x + 1 } + \frac { 3 } { x ^ { 2 } + 2 x + 1 }$

Because the denominators are the same, simply add the numerators.

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

To get a common denominator:

$\text{Multiply the first fraction by } \frac{x-1}{x-1}$

$\text{and the second fraction by } \frac{x-2}{x-2}.$

When subtracting, distribute the negative to all terms in the numerator of the second fraction.