# Worksheet: Simplifying Rational Functions

In this worksheet, we will practice simplifying rational functions and finding their domains.

**Q4: **

Simplify the function , and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q5: **

Given that and , find the largest set on which the functions and are equal.

- A
- B
- C
- D
- E

**Q6: **

Given the functions and , what is the set of values on which ?

- A
- B
- C
- D
- E

**Q7: **

Which of the following statements describes when two functions and are equal?

- A
- B the domain of the domain of
- C the domain of the domain of and
- Dthe domain of the domain of and for each in the common domain

**Q8: **

Simplify the function and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q9: **

Simplify the function and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q10: **

Simplify the function , and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q11: **

Simplify the function , and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q12: **

Simplify the function , and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q13: **

Given that the algebraic fraction simplifies to , what is the value of ?

**Q14: **

Given that , , and , find if possible.

- A
- B4
- C
- D
- E64

**Q15: **

Given that simplifies to , what is the value of ?

**Q16: **

Simplify the function , and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q17: **

Given that the functions and are equal, what are the values of and ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q18: **

Which of the following functions are equal?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q19: **

Simplify the function and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q20: **

Which of the following functions are equal?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q21: **

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

**Q22: **

Given the functions and , what is the set of values on which ?

- A
- B
- C
- D
- E

**Q23: **

Given that the multiplicative inverse of the function is , find the value of .

**Q24: **

Determine the domain of the function .

- A
- B
- C
- D
- E

**Q25: **

Simplify the function and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain