Worksheet: Solving Rational Equations Using the Least Common Denominator

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In this worksheet, we will practice solving rational equations by eliminating their denominators using the least common denominator.

Q1:

What value of 𝑥 solves the equation 𝑥 − 5 4 − 1 = 𝑥 2 ?

Q2:

Solve 𝑥 − 3 4 + 1 3 = 2 𝑥 + 3 2 for 𝑥 .

  • A − 2 4 9
  • B 2 3 9
  • C 2 4 9
  • D − 2 3 9
  • E − 1 4 9

Q3:

Find the solution set of the equation

  • A { 5 , − 5 }
  • B { 5 }
  • C { 2 }
  • D ∅
  • E { − 4 }

Q4:

Given that 7 𝑥 𝑥 − 3 = 1 6 𝑥 𝑥 + 3 − 9 , find the value of 𝑥 .

  • A 2 7 1 1
  • B 2 7 5
  • C 2 7 1 7
  • D 2 7 2 3
  • E3

Q5:

Given that 2 √ 𝑥 − √ 1 1 = 2 √ 𝑥 + √ 1 1 + 2 √ 1 1 , find the value of 𝑥 .

  • A22
  • B11
  • C0
  • D33
  • E 5 5 2

Q6:

Simplify the function 𝑛 ( 𝑥 ) = 5 𝑥 − 1 5 𝑥 𝑥 + 2 𝑥 − 1 5 𝑥 − 3 6 − 𝑥 𝑥 − 𝑥 − 3 0 2 4 3 2 2 2 , then find the solution set of the equation 𝑛 ( 𝑥 ) = 0 .

  • A 𝑛 ( 𝑥 ) = 𝑥 − 1 𝑥 , solution set = { 1 }
  • B 𝑛 ( 𝑥 ) = 𝑥 + 1 𝑥 , solution set = { 0 }
  • C 𝑛 ( 𝑥 ) = 𝑥 − 1 𝑥 , solution set = { 0 }
  • D 𝑛 ( 𝑥 ) = 𝑥 + 1 𝑥 , solution set = { − 1 }
  • E 𝑛 ( 𝑥 ) = ( 𝑥 + 1 ) 𝑥 ( 𝑥 − 1 ) 2 , solution set = { − 1 }

Q7:

What is the solution set of the equation 1 𝑥 − 1 − 1 𝑥 = 1 𝑥 − 1 𝑥 + 1 ?

  • A { 0 }
  • B { 2 }
  • C { 1 }
  • D { }
  • E { − 1 }

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