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SAT Math skill page

SAT Rational Equations Practice

Clear denominators carefully, solve the resulting equation, and reject values that make a denominator zero.

Practice rational equations in Dolphin SATPractice questions
12-18 min practice time3 questions on pageAdvanced Math
Practice time12-18 min
Question bank3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
If x/3 = 4, what is the value of x?
  1. 1
  2. 7
  3. 12
  4. 16
Show answer and solution
Correct answerC. 12

Solution walkthrough

  1. Multiply both sides by 3 to clear the denominator: x = 12.
Question 2 of 3Medium
If 2/(x - 1) = 1, what is the value of x?
  1. 1
  2. 2
  3. 3
  4. 4
Show answer and solution
Correct answerC. 3

Solution walkthrough

  1. Multiply by x - 1 to get 2 = x - 1, so x = 3.
  2. This does not make the denominator zero.
Question 3 of 3Hard
If 3/x = 1/(x - 2), what is the value of x?
  1. -3
  2. 0
  3. 2
  4. 3
Show answer and solution
Correct answerD. 3

Solution walkthrough

  1. Cross-multiply to get 3(x - 2) = x.
  2. Then 3x - 6 = x, so 2x = 6 and x = 3.

Avoid these traps

Common mistakes on this skill

Forgetting excluded values

Any value that makes an original denominator zero cannot be a solution.

Clearing only one denominator

Multiply every term on both sides by the least common denominator.

Checking only the simplified equation

Substitute the result into the original rational equation to verify it remains defined.

Study plan

How to practice this skill in Dolphin

  1. Write the values that make any denominator zero.
  2. Find the least common denominator and multiply every term by it.
  3. Solve the resulting polynomial or linear equation.
  4. Reject excluded values and verify the remaining solution.
Practice rational equations in Dolphin SAT

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SAT Radical Equations PracticeSAT Equivalent Expressions PracticeSAT Linear Equations PracticeSAT Math skill hub

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FAQ

Questions about SAT Rational Equations Practice

What is a rational equation?

It is an equation containing one or more fractions whose numerator or denominator includes an algebraic expression.

Why do rational equations have excluded values?

Division by zero is undefined, so values that make an original denominator zero are not allowed.

Should I cross-multiply every rational equation?

Cross-multiplication works for one fraction equal to one fraction. With more terms, clearing all denominators is usually safer.