﻿ Adding and Subtracting Fractions With Variables
ADDING AND SUBTRACTING FRACTIONS WITH VARIABLES
• PRACTICE (online exercises and printable worksheets)

To add or subtract fractions:

• You must have a common denominator.
• To find the Least Common Denominator (LCD),
take the least common multiple of the individual denominators.
• Express each fraction as a new fraction with the common denominator,
by multiplying by one in an appropriate form.
• To add fractions with the same denominator:
add the numerators, and keep the denominator the same.
That is, use the rule: $$\frac{A}{C} + \frac{B}{C} = \frac{A+B}{C}$$

EXAMPLE:
Question:
Combine into a single fraction:   $\displaystyle \frac{2}{x+3} - \frac{3x}{x-1}$
Solution:
Note that the LCD is $\,(x+3)(x-1)\,$.
 $\displaystyle\frac{2}{x+3} - \frac{3x}{x-1}$ (original expression) $\displaystyle\ \ = \frac{2}{x+3}\cdot\frac{x-1}{x-1} - \frac{3x}{x-1}\cdot\frac{x+3}{x+3}$ (get a common denominator by multiplying by $\,1\,$) $\displaystyle\ \ = \frac{2(x-1)-3x(x+3)}{(x+3)(x-1)}$ (keep the denominator the same; add the numerators) $\displaystyle\ \ = \frac{2x-2-3x^2 - 9x}{(x+3)(x-1)}$ (multiply out the numerator) $\displaystyle\ \ = \frac{-3x^2 - 7x - 2}{(x+3)(x-1)}$ (combine like terms; write numerator in standard form)
Leave the denominator in factored form for your final answer.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Writing expressions involving percent increase and decrease

CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
AVAILABLE MASTERED IN PROGRESS
 Combine into a single fraction:
 (MAX is 22; there are 22 different problem types.)