ADDING AND SUBTRACTING FRACTIONS WITH VARIABLES

To add or subtract fractions:

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.)