Simplify Expressions with Rational Numbers

Adding and Subtracting Rational Expressions

by Mrs. Berkner

Multiple Choice

Simplify the expression

• 6x / 20xy
• 3 / 10y
• (6x+1) / (20xy)
• 3 / 20xy

Multiple Choice

Simplify the expression

• (2a + 4b) / 12b²
• (2a - 4b) / 12b² 
• (a - b) / 6b²
• (a + 2b) / 6b² 

Multiple Choice

Multiple Choice

Multiple Choice

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

• $$\frac{-2x-10}{3x+4};\ x\ne-\frac{4}{3}$$  

• $$\frac{-2x}{3x+4};\ x\ne-\frac{4}{3}$$  

• $$-2x;\ x\ne0$$  

• $$-2x-10;\ x\ne0$$  

Multiple Choice

Multiple Choice

Multiple Choice

Subtract $$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$$  

• $$\frac{x^2-2x-8}{2x+7};\ x\ne-\frac{7}{2}$$  

• $$x^2-2x-8;\ x\ne0$$  

• $$x^2-2x+2;\ x\ne0$$  

• $$\frac{x^2-2x+2}{2x+7};\ x\ne-\frac{7}{2}$$  

Multiple Select

What do you have to do when adding or subtracting rational expressions? Check all that apply.

• Find a common denominator

• Simplify completely

• Solve for x

• Distribute the negative when subtracting

• nothing

Multiple Choice

Find the least common denominator of the expression

• 18
• 6x
• 3xy
• 6xy

Multiple Choice

Simplify the expression

• (5x + 4y) / 9y
• (6y + 3x) / 3y
• (2y + x) / y
• (6y + 3x) / 9y 

Multiple Choice

Simplify the expression

• (-17x - 12y) / 15x

• (23x - 4y) / 15x

• (-17x - 4y) / 15x

• (-3x - 4y) / 8x

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Multiple Choice

Multiple Choice

Add $$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$$  

• $$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$$  

• $$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ 1$$  

• $$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$$  

• $$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-\frac{1}{4},\ 2$$  

Multiple Choice

Subtract $$\frac{x}{2x+3}-\frac{2x+1}{2x-3}$$  

• $$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{2}{3}$$  

• $$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{3}{2}$$  

• $$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{3}{2}$$  

• $$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{2}{3}$$  

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Subtract, factor, simplify

• A
• B
• C
• D

Poll

How confident are you with adding/subtracting rational expressions?