Add and subtract rational expressions

Learning Objectives Identify the Least Common Denominator (LCD) of two or more rational expressions by factoring polynomials. Add rational expressions with like denominators and simplify the result. Subtract rational expressions with like denominators, correctly distributing the negative sign to all terms in the second numerator. Add rational expressions with unlike denominators by creating equivalent expressions with the LCD. Subtract rational expressions with unlike denominators by creating equivalent expressions with the LCD. Simplify the sum or difference of rational expressions by factoring and canceling common factors. State the non-permissible values (domain restrictions) for any addition or subtraction problem involving rational expressions. If you can paint a room...

TermDefinitionExample Rational ExpressionA fraction in which the numerator and the denominator are polynomials. The value of the polynomial in the denominator cannot be zero.(x^2 + 2x + 1) / (x - 3), where x ≠ 3 Least Common Denominator (LCD)The smallest polynomial that is a multiple of all the denominators in a set of rational expressions. It is found by taking the product of the highest power of each unique factor from all denominators.For 1/(x-2) and 1/(x^2-4), the denominators factor to (x-2) and (x-2)(x+2). The LCD is (x-2)(x+2). Like DenominatorsWhen two or more rational expressions have the exact same polynomial in their denominators.(3x)/(x+5) and (7)/(x+5) have like denominators. Unlike DenominatorsWhen the denominators of two or more rational expressions are different polynomial...

Addition/Subtraction with Like Denominators P/Q + R/Q = (P + R)/Q, P/Q - R/Q = (P - R)/Q If the denominators are the same, simply add or subtract the numerators and place the result over the common denominator. Always place the second numerator in parentheses when subtracting. Procedure for Unlike Denominators 1. Factor all denominators. 2. Find the LCD. 3. Create equivalent expressions with the LCD. 4. Add or subtract the numerators. 5. Simplify. This is the fundamental process for adding or subtracting any rational expressions with different denominators. The goal is to transform the problem into one with like denominators.