Worksheet: Simplifying Complex Fractions Involving Polynomials

In this worksheet, we will practice simplifying algebraic fractional functions and determining their domain.

Q1:

Simplify the function 𝑛 ( 𝑥 ) = 7 𝑥 + 𝑥 + 6 3 𝑥 + 6 9 𝑥 + 6 , and find its domain in .

  • A 𝑛 ( 𝑥 ) = 7 , domain =
  • B 𝑛 ( 𝑥 ) = 7 , domain = { 6 }
  • C 𝑛 ( 𝑥 ) = 1 7 , domain = { 6 , 3 }
  • D 𝑛 ( 𝑥 ) = 7 , domain = { 6 , 3 }
  • E 𝑛 ( 𝑥 ) = 1 7 , domain = { 6 }

Q2:

Simplify 3 + 1 completely.

  • A 3 𝑥 + 1 5 𝑥 2 5
  • B 𝑥 5 3 𝑥
  • C 𝑥 𝑥 5
  • D 3 𝑥 𝑥 5
  • E 3 𝑥 5

Q3:

Simplify the function 𝑛 ( 𝑥 ) = 2 𝑥 + 3 𝑥 + 9 8 𝑥 + 1 4 1 4 7 𝑥 + 1 4 , and find its domain in .

  • A 𝑛 ( 𝑥 ) = 2 3 , domain =
  • B 𝑛 ( 𝑥 ) = 2 3 , domain = { 1 4 }
  • C 𝑛 ( 𝑥 ) = 3 2 , domain = { 1 4 , 7 }
  • D 𝑛 ( 𝑥 ) = 2 3 , domain = { 1 4 , 7 }
  • E 𝑛 ( 𝑥 ) = 3 2 , domain = { 1 4 }

Q4:

Simplify the function 𝑛 ( 𝑥 ) = 6 𝑥 + 3 𝑥 + 1 5 0 𝑥 1 0 7 5 𝑥 1 0 , and find its domain in .

  • A 𝑛 ( 𝑥 ) = 2 , domain =
  • B 𝑛 ( 𝑥 ) = 2 , domain = { 1 0 }
  • C 𝑛 ( 𝑥 ) = 1 2 , domain = { 5 , 1 0 }
  • D 𝑛 ( 𝑥 ) = 2 , domain = { 5 , 1 0 }
  • E 𝑛 ( 𝑥 ) = 1 2 , domain = { 1 0 }

Q5:

Simplify the function 𝑛 ( 𝑥 ) = 𝑥 + 4 𝑥 + 4 9 𝑥 1 4 1 9 6 𝑥 1 4 , and find its domain in .

  • A 𝑛 ( 𝑥 ) = 1 4 , domain =
  • B 𝑛 ( 𝑥 ) = 1 4 , domain = { 1 4 }
  • C 𝑛 ( 𝑥 ) = 4 , domain = { 7 , 1 4 }
  • D 𝑛 ( 𝑥 ) = 1 4 , domain = { 7 , 1 4 }
  • E 𝑛 ( 𝑥 ) = 4 , domain = { 1 4 }

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