ADDING AND SUBTRACTING FRACTIONS WITH VARIABLES
• PRACTICE (online exercises and printable worksheets)

• 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)
Master the ideas from this section

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

CONCEPT QUESTIONS EXERCISE: