# Worksheet: Rational Equations

In this worksheet, we will practice solving rational equations.

**Q3: **

What is the solution set of the equation ?

- A
- B
- C
- D
- E

**Q5: **

Find the value of that makes equal to zero.

**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

**Q15: **

Find the value of given is the multiplicative inverse of .

- A
- B
- C
- D

**Q18: **

It takes Victoriaββ2 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

**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