Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Numbers

• 1. In order to add or subtract fractions, they must have a common denominator

• 2. The lowest common denominator is the smallest number that is a multiple of all of the denominators

Adding and Subtracting Rational Numbers

• 3. Once the lowest common denominator is found, rewrite all of the fractions as equivalent fractions with that denominator

• 4. Then add (or subtract) numerators, and keep the common denominator

Multiple Choice

What is the lowest common denominator of 1/2, 1/3, 1/5?

• 12

• 6

• 30

• 5

Multiple Choice

What is the lowest common denominator of 9, 8, 12?

• 56

• 64

• 108

• 72

Multiple Choice

What is the equivalent fraction for 3/8 if the common denominator is 24?

• 6/24

• 4/24

• 9/24

• 12/32

Adding Rational Expressions with the Same Denominator

• 1. if the denominators of the expressions you are trying to add are the same, simply add the numerators and keep the common denominator

• Simplify the numerator by combining like terms

• Factor the numerator and denominator to see if the expression can be reduced

Multiple Choice

Simplify the expression

• (2a + 4b) / 12b²

• (2a - 4b) / 12b²

• (a - b) / 6b²

• (a + 2b) / 6b²

Multiple Choice

Simplify the expression

• n / 2m

• n / 3m

• (m² + 4n²) / 12m

• n / 4m

Multiple Choice

Simplify the expression

• 6x / 20xy

• 3 / 10y

• (6x+1) / (20xy)

• 3 / 20xy

Adding or Subtracting Rational Expressions with Different Denominators

• 1. Before you can combine rational expressions, they must have a common denominator

• 2. Check to see if the smaller denominator is a factor of the larger denominator

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Adding and Subtracting Rational Expressions with Different Denominators

• 3. If one denominator appears as a factor in another denominator, you don't have to repeat that expression in the common denominator

• 4. The lowest common denominator must contain factors that appear in all the denominators

Adding or Subtracting Rational Expressions with Different Denominators

• 5. Once you have decided upon the common denominator, rewrite each expression as an equivalent fraction with the new denominator

• 6. Simplify by combining like terms in the numerator

• 7. Factor the numerator and denominator

• 8. Reduce by canceling like terms.

Multiple Choice

What is the common denominator when simplifying  $\frac{4}{x+8}+\frac{3}{x-5}$  

•  $x^2-40$  

•  $2x+3$  

•  $\left(x+8\right)+\left(x-5\right)$  

•  $\left(x+8\right)\left(x-5\right)$  

Multiple Choice

Which is the next correct setup for simplifying  $\frac{7x}{x+1}+\frac{2}{x-3}$  

•  $\frac{7x}{x+1}\cdot\frac{2}{x-3}+\frac{2}{x-3}\cdot\frac{7x}{x+1}$  

•  $\frac{7x}{x+1}\cdot\frac{7x}{x+1}+\frac{2}{x-3}\cdot\frac{2}{x-3}$  

•  $\frac{7x}{x+1}\cdot\frac{x-3}{x-3}+\frac{2}{x-3}\cdot\frac{x+1}{x+1}$  

•  $\frac{7x}{x+1}\cdot\frac{x+1}{x+1}+\frac{2}{x-3}\cdot\frac{x-3}{x-3}$  

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Simplify

• (x-9)/(x+9)

• 1/(x-9)

• (x+9)

• 1/(x+9)

Multiple Choice

Simplify

• (x-9)/(x+9)

• 1/(x-9)

• (x+9)

• 1/(x+9)

Multiple Choice

Simplify the expression

• (-17x - 12y) / 15x

• (23x - 4y) / 15x

• (-17x - 4y) / 15x

• (-3x - 4y) / 8x