Adding and Subtracting Fractions With Variables
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:
$$
\cssId{s12}{\frac{2}{x+3}  \frac{3x}{x1}}
$$
Solution:
Note that the LCD is $\,(x+3)(x1)\,.$
$\displaystyle\frac{2}{x+3}  \frac{3x}{x1}$  original expression 
$\displaystyle
= \frac{2}{x+3}\cdot\frac{x1}{x1}
$
$\displaystyle \qquad \ \frac{3x}{x1}\cdot\frac{x+3}{x+3} $ 
get a common denominator by multiplying by $\,1\,$ 
$\displaystyle = \frac{2(x1)3x(x+3)}{(x+3)(x1)}$  keep the denominator the same; add the numerators 
$\displaystyle = \frac{2x23x^2  9x}{(x+3)(x1)}$  multiply out the numerator 
$\displaystyle = \frac{3x^2  7x  2}{(x+3)(x1)}$  combine like terms; write numerator in standard form 
Leave the denominator in factored form for your final answer.