Adding & Subtracting Rational Expressions with unlike denominators

Adding & Subtracting Rational Expressions with unlike denominators Objective Students will add/subtract rational expressions with unlike denominators by finding the LCD.

Warm-ups

We know that… • …in order to add or subtract fractions, there must be a common denominator. • …if a common denominator does not exist, we must find the LEAST COMMON DENOMINATOR (LCD). (aka LEAST COMMON MULTIPLE)

Find the LCM – The Bag Method Find the LCM between 12 & 18 18 12 2 2 3 2 3 3 3 4 2 9 3 3 2 2 Cross out duplicates The Smallest # both 12 & 18 Divide is 2x2x3x3 = 36

Find the LCM of Algebraic Expressions 3 3 x x y y 2 2 3 x x y Prime Factors of each term No duplicate factors LCM = (2)(2)(3)(3)(x)(x)(y)(y) = With LCMs, we take the largest exponent. With GCFs we took the smallest exponent.

Find the LCM on your own.

Finding LCMs of Polynomials • FACTOR FIRST LCM = (x – 4)(x – 1)(x + 1) (x – 4)(x – 1) (x – 4)(x + 1) Prime Factors of each term No duplicate factors

Find the LCM on your own. a LCM = (x – 3)(x – 2)(x + 5) b LCM = (x – 3)(x + 3)(x + 3)

Example: Add/Subtract (Monomial Denominators) Find LCD First! Equals 1 Creates a Common Denominator Now we can add numerators 2 3 x x 3 x

Example: Add/Subtract (Monomial Denominators) Equals 1 Creates a Common Denominator Now we can add numerators

Example Add/Subtract (Polynomial Denominators) Factor your numerator just in case you can simplify. In this case we cannot simplify, no common factors.

Example Add/Subtract (Polynomial Denominators) Factor First Find LCD Combine Numerators Factor Numerator Simplify

Example Add/Subtract (Polynomial Denominators) Factor First Find LCD Combine Numerators Simplify?

Example Add/Subtract (Polynomial Denominators) Factor First Find LCD Combine Numerators Distribute the Negative

Example Continued Distribute the Negative Combine Numerators Simplify?

Adding & Subtracting Rational Expressions with unlike denominators