# 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

$\dfrac{2(x+5)+3x(x+4)}{(x+2)(x+5)(x+4)} = \dfrac{3x^2+14x+10}{x^3+11x^2+38x+40}$

Write equivalent fractions with like denominators, add numerators, and simplify.