Adding and Subtracting Rational Expressions

WARM UP 1) Suppose y varies inversely with x, Write an equation that includes the point (4,2) 2) The length of a violin string varies inversely as the frequency of its vibrations. A violin string 14 in long vibrates at a frequency of 450 cycles per second. Find the frequency of a 12- in violin string.

Review Identify vertical and horizontal asymptotes and state domain and range 1)

Review of Multiplying Multiply the following:

Review of Dividing Divide the following:

Review of Adding and Subtracting Fractions With Common Denominators

Adding.

Subtracting.

9.5 Adding and Subtracting with Unlike Denominators

Common Denominator A Common Denominator is also the LEAST COMMON MULTIPLE. LCM is the smallest numbers that each factor can be divided into evenly. Finding LCM of 2 numbers: 7: 21:

LCM Find the LCM of each pair of numbers 1. 4, , , 12

Review of Adding and Subtracting Fractions With Unlike Denominators Add or subtract the following

Steps for Adding or Subtracting 1) Find a Common Denominator 1) Turn both fractions into equivalent fractions with the common denominator 2) Add or Subtract the top, and keep the bottom

Finding LCM For Variables LCM: Take the Largest Exponent! Find the LCM: x 4 and x x 3 and x 2 3x 5 and 9x 8

Adding and Subtracting Fractions With Unlike Denominators Add or subtract the following

Finding LCM of Expressions For Expressions LCM: Include ALL factors!! EX: 3(x + 2) and 5(x – 2) x(x + 4) and 3x 2 (x + 4) (x 2 + 2x - 8) and (x 2 – 4) 7(x 2 – 25) and 2(x 2 + 7x + 10)

Add or Subtract the Following 1.

Add or Subtract the Following 1.

Add or Subtract the Following 1.

Add or Subtract the Following 1.

Complex Fractions A complex fraction is a faction that has a fraction in its numerator or denominator.

Simplifying To Simplify Multiply the top and the bottom by the COMMON DENOMINATOR

Try Some! Simplify