7.3: Addition and Subtraction of Rational Expressions Algebra 2A 7.3: Addition and Subtraction of Rational Expressions September 27, 2006

Objectives Students will be able to: Add and subtract rational expressions Add and subtract rational functions

Adding and Subtracting fractions In order to be able to add or subtract straight across fraction, they must have the same denominator! So… P + Q = P+Q R R R And P - Q = P-Q

An example with the same denominator 3 - 1 + 5 = 2a2 2a2 2a2 = 3-1+5 2a2 = 7

Another example 3y + y + 5y = 2x2 2x2 2x2

What if you can simplify? After adding, if it is possible to simplify by factoring, please do! For example: 5x + 15 x2-9 x2-9 = 5x+15 x2-9 =5(x+3) (x+3)(x-3) = 5 x-3

Practice with the same denominator and simplifying a2-2a-8 a2-2a-8

What if the denominators are different? Then you must find the least common denominator (LCD) Write each denominator in completely factored form Write the LCD as a product of each prime factor to the highest power that appears in either denominator For example: 3 and 5 4x2 6xy 4x2 = 22 * x2 6xy = 2 * 3 * x * y The LCD must have 22 * 3 * x2 LCD = 12x2y

How do I use the LCD? 3 + 5 LCD= 12x2y 4x2 6xy Then rewrite the each expression so the denominator is the LCD. (3y) 3 + (2x) 5 (3y) 4x2 (2x) 6xy 9y + 10x 12x2y 12x2y = 9y+10x 12x2y

What if the LCD is harder to find? -5 + 8 x2-3x-4 x2-16 (x-4)(x+1) (x+4)(x-4) (x+4) -5 + (x+1) 8 (x+4) (x-4)(x+1) (x+1) (x+4)(x-4) -5x-20 + 8x+8 = 3x-12 (x+4) (x-4)(x+1) (x+1)(x+4)(x-4) (x+4) (x-4)(x+1) 3(x-4) (x+4) (x-4)(x+1) 3 (x+4)(x+1)

More about subtracting What if a whole number is involved? - 5 2x-1 3 - 5 (2x-1) 3 - 5 (2x-1) 1 2x-1 6x-3 - 5 2x-1 2x-1 = 6x-8

Adding and subtracting rational functions h(x) = f(x) - g(x) h(x) = f(x) + g(x) Use the same steps as you used with adding and subtracting rational expressions. Make sure that your signs are correct! Remember h(1) just means plug in x=1. Evaluate means solve….