# Worksheet: Rational Equations

In this worksheet, we will practice solving rational equations.

Q1:

Find the solution set of the equation

• A
• B
• C
• D
• E

Q2:

Given that , find the value of .

• A
• B
• C3
• D
• E

Q3:

What is the solution set of the equation ?

• A
• B
• C
• D
• E

Q4:

Solve the equation .

• A
• B
• C
• D
• E

Q5:

Find the value of that makes equal to zero.

Q6:

Solve .

• A
• B
• C
• D
• E

Q7:

Solve the equation .

• A
• B
• C
• D
• Eno solution

Q8:

Solve .

• A
• B
• Cno solution
• D
• E

Q9:

Solve for .

• A,
• B,
• C,
• D,
• E,

Q10:

If , find the value of .

Q11:

Find the solution set of in .

• A
• B
• C
• D

Q12:

Find given .

Q13:

Solve .

• A
• B
• C
• D
• E

Q14:

Solve .

• A
• B
• C
• D
• E

Q15:

Find the value of given is the multiplicative inverse of .

• A
• B
• C
• D

Q16:

Liam went on a bike ride of 48 miles. He realized that if he had gone 4 mph faster, then he would have arrived 6 hours sooner. How fast did he actually ride?

Q17:

If Victoria does a job in 10 hours, and with the help of Scarlett, they can do it together in 6 hours, how long would it take Scarlett to do it alone?

Q18:

It takes Victoria  2 hours to pick up 8 kg of strawberries. When she is helped by her son, Ethan, it takes them 1 hour and a quarter. How long would it take Ethan to pick up 8 kg of strawberries alone? Give your answer in hours and minutes.

• A3 hours and 20 minutes
• B2 hours and 45 minutes
• C2 hours and 30 minutes
• D3 hours and 45 minutes
• E3 hours and 15 minutes

Q19:

A speech therapist charges two different fees, \$20 and \$35, depending on the type of the session. On a given day, she has already had 3 sessions at \$20 and 4 at \$35. For the rest of the day, she will only have sessions at \$20. How many of those should she give to earn an average rate of \$25 per session?

Q20:

Consider the equation

If you multiply both sides by and rearrange so that the right-hand side is 0, what equation do you get?

• A
• B
• C
• D
• E

What can you say about the solutions of the original equation?

• Athere are two solutions
• Bthere are no solutions
• Cevery value of is a solution
• Dthere is only one solution

Q21:

For what value of does the equation have no solutions?

Q22:

Find the solution set of in .

• A
• B
• C
• D
• E

Q23:

Find the solution set of in .

• A
• B
• C
• D
• E

Q24:

Given that the multiplicative inverse of is , what is the value of ?

Q25:

Given that is a rational number and , find all the possible values of .

• A
• B
• C
• D