Rational Expressions and Equations Chapter 6 Rational Expressions and Equations

Complex Rational Expressions 6.5 Using Division to Simplify Multiplying by the LCD

To Simplify a Complex Rational Expression by Dividing 1. Add or subtract, as needed, to get a single rational expression in the numerator. 2. Add or subtract, as needed, to get a single rational expression in the denominator. 3. Divide the numerator by the denominator (invert and multiply). 4. If possible, simplify by removing a factor equal to 1.

Simplify: Solution Rewriting with a division symbol Multiplying by the reciprocal of the divisor (inverting and multiplying) Factoring and removing a factor equal to 1.

Simplify: Solution Multiplying by 1 to get the LCD, 3, for the numerator. Multiplying by 1 to get the LCD, 2x, for the denominator. Adding Subtracting

Rewriting with a division symbol. This is often done mentally. Multiplying by the reciprocal of the divisor (inverting and multiplying)

To Simplify a Complex Rational Expression by Multiplying by the LCD 1. Find the LCD of all rational expressions within the complex rational expression. 2. Multiply the complex rational expression by a factor equal to 1. Write 1 as the LCD over itself (LCD/LCD). 3. Simplify. No fractional expressions should remain within the complex rational expression. 4. Factor and, if possible, simplify.

Solution Here we look for the LCD of all four factors. Simplify: Solution Here we look for the LCD of all four factors. Multiplying by a factor equal to 1, using the LCD: 12/12=1 Multiplying the numerator by 12 Don’t forget the parentheses! Multiplying the denominator by 12

Using the distributive law Simplifying

Simplify: Solution The LCD is x. When we multiply by x, all fractions in the numerator and denominator of the complex rational expression are cleared: Using the distributive law

Simplify: Solution The LCD is x3 so we multiply by 1 using x3/x3. Using the distributive law All fractions have been cleared and simplified.