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Worksheet: Solving Rational Equations Using the Least Common Denominator

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

Q1:

Given that 7 π‘₯ π‘₯ βˆ’ 3 = 1 6 π‘₯ π‘₯ + 3 βˆ’ 9 , find the value of π‘₯ .

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

Q2:

What is the solution set of the equation 1 π‘₯ βˆ’ 1 βˆ’ 1 π‘₯ = 1 π‘₯ βˆ’ 1 π‘₯ + 1 ?

  • A { 0 }
  • B { 2 }
  • C { 1 }
  • D { }
  • E { βˆ’ 1 }

Q3:

Solve the equation 1 2 = 2 3 π‘₯ βˆ’ 1 .

  • A π‘₯ = 1 4
  • B π‘₯ = 9 4
  • C π‘₯ = 1 9
  • D π‘₯ = 4 9
  • E π‘₯ = 3 5

Q4:

Find the value of that makes equal to zero.

Q5:

Solve 2 π‘₯ + 1 3 = 1 .

  • A π‘₯ = 1 3
  • B π‘₯ = 1
  • C π‘₯ = 0
  • D π‘₯ = 3
  • E π‘₯ = 2 3

Q6:

Solve the equation 8 π‘š βˆ’ 1 + 4 π‘š + 1 = βˆ’ 8 π‘š βˆ’ 1 2 .

  • A π‘š = βˆ’ 2
  • B π‘š = βˆ’ 1
  • C π‘š = 0
  • Dno solution
  • E π‘š = 1

Q7:

Solve 3 𝑛 βˆ’ 4 + 1 𝑛 + 2 = 2 𝑛 βˆ’ 2 2 .

  • A 𝑛 = 2
  • B 𝑛 = 3
  • C 𝑛 = βˆ’ 2
  • D 𝑛 = βˆ’ 3
  • E no solution

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