Solving Rational Equations

Solve for x:
 $\frac{2}{x+2}+\frac{5}{x-2}=\frac{6}{x^2-4}$  

• x = 7

• x = 6

• x = 14

• x = 0

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

Solve:  $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$  

•  $x=-5$  

•  $x=5$  

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

• No Solution

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

Solve for x:  $\frac{6x+18}{x^2}+\frac{1}{x}=\frac{3}{x}$  

• x = 9/2
  

• x = -9/2

• x = 3

• x = -3

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

Solve for x:
 $\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}$  

• x = 5

• x = $\frac{4}{5}$

• x = 1

• x = - 4

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

Solve for x:

 $2-\frac{1}{x^2+x}=\frac{3}{x+1}$  

•  $x\ =\ 1$  

•  $x=-\frac{1}{2}$  

•  $x=\left\{-\frac{1}{2},\ 1\right\}$  

• No Solution
  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Solve for x:

 $\frac{x}{x+2}+\frac{2}{x^2+5x+6}=\frac{5}{x+3}$  

•  $x=4$  

•  $x=-2$  

•  $x=\left\{-2,\ 4\right\}$  

• No Solution
  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

It takes two farmers 5 hours to plow a field when they work together. If Farmer A can plow the field in 9 hours when working alone, how long will it take Farmer B to plow the field on his own?

• 11.25 hours

• 0.1 hours

• 0.3 hours

• 3.5 hours

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Garrett can row 5 miles per hour in still water. It takes him the same amount of time to row 4 miles upstream as it does to row 16 miles downstream. What is the speed of the current?

• 4 mph

• 3 mph

• 2.4 mph

• 2.86 mph

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Miranda swims 11 miles downstream in the same time she can swim 7 miles upstream. If the speed of the current is 4 miles per hour, how fast can Miranda swim in still water?

• 4.5 mph

• 1 mph

• 12 mph

• 18 mph

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

When the same number is subtracted from the denominator of  $\frac{5}{7}$  is added to its numerator, the resulting fraction is  $\frac{1}{3}$ .  Find the number.

• -2

• -4

• 2

• 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1