dolphin
Get Started

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
Practice questions3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin practice questions

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

Dolphin Web gives you a personalized SAT study plan with lessons, unlimited Pip AI help, practice questions, full-length tests, and mistake review. The iPhone and Android apps are free. See plans.

  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

Related practice

Build the surrounding skills

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

Skill cluster

Keep practicing SAT Math

SAT Math skill hubDesmos calculator walkthroughsSAT Linear Equations PracticeSAT Systems of Equations PracticeSAT Linear Functions PracticeSAT Quadratic Equations PracticeSAT Percentages PracticeSAT Ratios and Proportions PracticeSAT Probability PracticeSAT Geometry PracticeSAT Right Triangles PracticeSAT Data Analysis PracticeSAT Circle Equations PracticeSAT Exponential Functions PracticeSAT Inequalities PracticeSAT Equivalent Expressions PracticeSAT Systems of Inequalities PracticeSAT Absolute Value Equations PracticeSAT Function Notation PracticeSAT Polynomials PracticeSAT Scatterplots PracticeSAT Mean and Median PracticeSAT Unit Conversions PracticeSAT Exponent Rules PracticeSAT Quadratic Word Problems PracticeSAT Systems Word Problems PracticeSAT Slope-Intercept Form PracticeSAT Area and Volume PracticeSAT Percent Change PracticeSAT Trigonometry PracticeSAT Radical Equations PracticeSAT Conditional Probability PracticeSAT Sampling and Margin of Error PracticeSAT Statistical Claims PracticeSAT Reading and Writing Practice PagesDolphin SAT study guidesSAT score guides by college

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.