Adding Rational Expressions
The strategy for adding rational numbers also works for adding and subtracting rational expressions.
One example of the addition of rational expressions is:
\[\dfrac2{x^2+6x+8}+\dfrac{3x}{x^2+7x+10}=\]
Factor denominators
\[\dfrac{2}{(x+2)(x+4)} + \dfrac{3x}{(x+2)(x+5)}=\]
Find common denominator
\[\dfrac{2(x+5)+3x(x+4)}{(x+2)(x+5)(x+4)} = \dfrac{3x^2+14x+10}{x^3+11x^2+38x+40}\]
Finish by writing equivalent fractions with like denominators, adding numerators, and then simplify.
Watch the following Khan Academy Videos for more examples:
