Solving Rational Equations & Word Problems

What is the LCD for  $\frac{2}{x}+\frac{5}{x+3}=\ \frac{1}{x}$  ?

•  $x^2$  

•  $x\left(x+3\right)$  

•  $x+3$  

•  $2x\left(x+3\right)$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Solve for x:  $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$  

•  $2$  

•  $\frac{18}{5}$  

•  $\frac{26}{5}$  

•  $6$  

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

 $\frac{1}{2v^2}=\frac{1}{3v}+\frac{1}{6v^2}$  

• 1

• 5

• -2

• -1

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

Solve! $\frac{x+2}{8}=\frac{3}{4}$  

•  $x=2$  

•  $x=6$  

•  $x=4$  

•  $x=8$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

What is the least common multiple of x²-16 and x²+4x-32?

• (x + 4)(x – 4)(x + 8)

• (x-4)2 (x+8)

• (x + 4)(x – 4)

• (x - 4)(x-4)2(x + 8)

If it take Jayson 8 hours to build a shed, how much of the shed can he build per hour?

• $\frac{1}{8}$

• $8$

• $\frac{1}{2}$

• not enough information

Tags

CCSS.7.RP.A.1

CCSS.7.RP.A.2

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

• 48 minutes
• 50 minutes
• 24 minutes
• 12 minutes

Tags

CCSS.HSA.CED.A.1

Which of the following equations makes the most sense for the following situation: Jerry works twice as fast as Kenny. If Jerry works for 2 hours and is then joined by Kenny...and they work an additional 3 hours...how fast could they each do the job alone?

• $\frac{5}{x}+\frac{3}{2x}=1$

• $\frac{5}{2x}+\frac{3}{x}=1$

• $\frac{x}{3}+\frac{2x}{5}=1$

• $\frac{5}{x}+\frac{3}{x-2}=1$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

One crew can sow a field of corn in 6 days. A different crew can do the same job in 3 days. If the slow crew works alone for 2 days and then is joined by the faster crew, how long will it take them to finish?

• $\frac{3}{4}$ of a day longer

• $2\frac{1}{2}$ more days

• not enough information to tell

• $1\frac{1}{3}$ days longer

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.1

CCSS.7.NS.A.2

CCSS.7.NS.A.3

CCSS.7.RP.A.3

One computer can process payroll in 4 hours and a different computer can process it in 6 hours. If they start working at 10:00 a.m., when will they be done?

• 11:30 a.m.

• 1:00 p.m.

• 12:24 p.m.

• 12:48 p.m.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1