### Home > CCA2 > Chapter 6 > Lesson 6.1.5 > Problem6-83

6-83.

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.

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

To get a common denominator:

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

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.