Adding 3/(x + 2) + 2/(x - 1)

Algebra 1 · Axiom Academy

EXAMPLE Adding Rational Expressions Add two rational expressions by finding the LCD, rewriting with a common denominator, and combining numerators. Add the rational expressions and write the result as a single simplified fraction. Nice work — you added two rational expressions with unlike denominators. The process: Find the LCD: when the denominators share no common factor, the LCD is just their product, here (x+2)(x-1) . Rewrite each fraction: multiply numerator and denominator by the factor it's missing — a form of 1 that doesn't change the value. Combine numerators: once the denominators match, add the numerators and keep the common denominator. Simplify: expand and combine like terms, 3(x-1)+2(x+2)=5x+1 . Result: — already in lowest terms, since 5x+1 shares no factor with the denominator. This same routine — LCD, rewrite, combine, simplify — adds any pair of rational expressions.

This is the written version of the interactive lesson above. See the full Algebra 1 course.