Solving Rational Equations

For what value(s) of  $m$  is the expression  $\frac{m^2-2m+1}{2m^2+m-3}$  undefined?

•  $-\frac{3}{2},\ 0,\ 1$  

•  $-1,\ \frac{3}{2}$  

•  $-\frac{3}{2},\ 1$  

•  $\frac{3}{2}$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.7

Simplify the following expression: $\frac{x^2+5x+4}{x^2+2x+1}\times\frac{2x+2}{x+4}$  

•  $\frac{1}{2}$  

•  $2$  

•  $\frac{\left(x+4\right)^2}{2\left(x+1\right)^2}$  

•  $\frac{x+4}{2\left(x+1\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the following expression:
 $\frac{a+b}{3}\div\frac{a^2+b^2}{12}$  

•  $\frac{a+b}{4\left(a^2+b^2\right)}$  

•  $\frac{4}{a+b}$  

•  $\frac{a+b}{4}$  

•  $\frac{4\left(a+b\right)}{a^2+b^2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

What is the equation(s) of the vertical asymptote(s) of the graph of $f\left(x\right)=\frac{x^2+5x+6}{x-1}$ ?

•  $x=1$  

•  $x=-2$  

•  $x=-2,\ x=-3$  

•  $f\left(x\right)=1$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.7

Which rational function is graphed?

• $\frac{3}{x+2}$

• $\frac{3}{x-2}$

• $\frac{x}{x+2}$

• $\frac{x}{x-2}$

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The distance a car can travel on a certain amount of fuel varies INVERSELY with its speed. If a car traveling 50 miles per hour can travel 300 miles on 10 gallons of fuel, how far could the car travel on 10 gallons of fuel at 60 miles per hour?

• 250 miles

• 360 miles

• 275 miles

• 300 miles

Solve  $\frac{n}{n-4}+n=\frac{12-4n}{n-4}$  

•  $n=-4,\ n=3$  

•  $n=-3,\ n=4$  

•  $n=-4$  

•  $n=3$  

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

Tomas can do a job in 4 hours. Julia can do the same job in 6 hours. How many hours will it take the two of them to do the job if they work together?

• 3.5 hours

• 2.4 hours

• 5 hours

• 2 hours

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.2

CCSS.7.NS.A.3

Solve the following equation for x:
 $\frac{12}{x}+\frac{3}{4}=\frac{3}{2}$  

• 16

• 4

• 5

• 8

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

Solve for s:
 $\frac{s}{s+2}+s=\frac{5s+8}{s+2}$  

• 2

• 4

• 6

• 8

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3