11-4

11-4

Adding and Subtracting Rational Expressions

Adding and Subtracting with Like Denominators

Ex:  $\frac{7}{4x}+\frac{3}{4x}=\frac{10}{4x}$  

 $=\frac{5}{2x}$  

Multiple Choice

Find the difference:

 $\frac{2x}{x^3-2}-\frac{1}{x^3-2}$  

•  $\frac{2x-1}{x^3-2}$  

•  $\frac{2x+1}{x^3-2}$  

•  $\frac{2x-1}{2x^3-4}$  

•  $\frac{2x+1}{2x^3-4}$  

Multiple Choice

Find the sum:

 $\frac{1}{x}+\frac{9}{x}=$  

•  $\frac{10}{x}$  

•  $\frac{10}{2x}$  

•  $\frac{5}{x}$  

•  $\frac{10}{x^2}$  

Multiple Choice

Simplify the expression:

 $\frac{6}{2}+\ \frac{3}{2v-6}$  

•  $\frac{6v-15}{2\left(v-3\right)}$  

•  $\frac{7v-18}{2\left(v-3\right)}$  

•  $\frac{4v-18+v^2}{2\left(v-3\right)}$  

•  $\frac{5}{-2+v}$  

Multiple Choice

Simplify the expression:

 $\frac{x+2}{x-5}+\frac{4x}{5}$  

•  $\frac{-10x+10+3x^2}{5\left(x-5\right)}$  

•  $\frac{-15x+10+4x^2}{5\left(x-5\right)}$  

•  $\frac{5x+15}{3x\left(x-5\right)}$  

•  $\frac{3x^2+9x}{5\left(x-5\right)}$  

Multiple Choice

Simplify the expression

• (-17x - 12y) / 15x

• (23x - 4y) / 15x

• (-17x - 4y) / 15x

• (-3x - 4y) / 8x

Multiple Choice

Find the LCD of these fractions.

• (x+2)(x-2)
• (x+2)(x+1)
• (x+2)(x-2)(x+1)
• (x-2)(x+1)

Multiple Choice

Find the LCD of the following rational expressions
 $\frac{2x}{x+1}$  and  $\frac{1}{x^2-1}$ 

• (x+1)(x-1)

• (x+1)² (x-1)

• (2x+2)

Multiple Choice

Find the least common denominator of the expression

• 18
• 6x
• 3xy
• 6xy

Multiple Choice

To simplify a rational expression, I should

• Eliminate common terms in the numerator and denominator.
• Combine like terms in the numerator and denominator.
• Factor the numerator and denominator and eliminate common factors.
• Find an LCD.

Multiple Choice

When adding and subtracting rational expressions, my first step should be to:

• Combine like terms in the numerators.
• Determine a Least Common Denominator.
• Factor all of the numerators and all of the denominators.
• Change the operator to multiplication and reciprocate the second fraction.

Multiple Choice

Multiple Choice

John can pack 100 boxes in 5 hours. Bill can pack 100 boxes in 8 hours. If they work together, how long will it take to pack 100 boxes?

• 3 hours and 20 min

• 3 hours and 5 min

• 2 hours and 35 min

• 4 hours and 13 min