Adding+and+Subtracting+Rational+Expressions

Adding and Subtracting Rational Expressions


 * < Standard & Assessment Anchor ||< M11.D.2.2.3 Simplify algebraic fractions. ||
 * < Objective ||< We will add and subtract rational expressions and simplify complex fractions. ||

Add or subtract. Identify any x-values for which the expression is undefined


 * [[image:http://latex.codecogs.com/gif.latex?%5Cfrac%7Bx-3%7D%7Bx&plus;4%7D&plus;%5Cfrac%7Bx-2%7D%7Bx&plus;4%7D]] ||  ||
 * [[image:http://latex.codecogs.com/gif.latex?%5Cfrac%7Bx-3&plus;x-2%7D%7Bx&plus;4%7D]] || Add the numerators ||
 * [[image:http://latex.codecogs.com/gif.latex?%5Cfrac%7B2x-5%7D%7Bx&plus;4%7D]] || Combine like terms ||

The expression is undefined at x = -4 since the denominator will be equal to 0 at this value of x.

If we have unlike denominators, we have to multiply both numerator and denominator by a factor with an equivalence of 1 that will result in common denominators.

We will probably have to factor the denominators to determine what we must multiply by to result in a common denominator. We also have to remember to identify any values of x that make the expression undefinefd -- that is, division by 0. Our first step is to find the least common multiple for each pair of factors. It might be a monomial, but it might also be a polynomial.

Find the least common multiple for the pair:

If we factor the trinomials, we can write