Adding and Subtracting Rational Numbers

​Adding and Subtracting Rational Expressions with same denominators

​Ex.

Multiple Choice

FIND THE SUM: $$\frac{-9}{12y}+\frac{1}{12y}$$  

• $$\frac{5}{6y}$$  

• $$\frac{-2}{3y}$$  

• $$\frac{2}{3y}$$  

Multiple Choice

$$\frac{3x+5}{x+4}+\frac{2x+15}{x+4}$$  

• 5

• $$\frac{x+5}{x+4}$$  

• $$\frac{5}{4}$$  

Multiple Choice

$$\frac{9}{7x}-\frac{5}{7x}$$  

• $$\frac{4}{7x}$$  

• $$\frac{1}{3x}$$  

Multiple Choice

$$\frac{x^2}{x-3}-\frac{9}{x-3}$$  

• $$x+3$$  

• $$x-3$$  

Multiple Choice

$$\frac{2x-5}{x+3}-\frac{-x+4}{x+3}$$  

• $$3$$  

• $$\frac{3x-9}{x+3}$$  

​Adding and Subtracting Rational Expressions with different denominators

​Factor the denominators

​Multiply each fraction by the missing factor/s in the denominator

​Perform the operation then simplify if possible.

​Example:

Multiple Choice

$$\frac{2}{5}-\frac{1}{15}$$  

• $$\frac{1}{10}$$  

• $$\frac{1}{3}$$  

• $$\frac{2}{5}$$  

Multiple Choice

$$\frac{-x}{2-x}-\frac{2}{x-2}$$  

• $$-1$$  

• $$1$$  

• $$\frac{x+2}{x-2}$$  

Multiple Choice

$$\frac{7}{9x^{2\ }}+\frac{x}{3x^2+3x}$$  

• $$\frac{3x^2+7x+7}{9x^{2\ }\left(x+1\right)}$$  

• $$\frac{10x^2+1}{9x^{2\ }\left(x+1\right)}$$