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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 SAT Try examples
12-18 min practice time 3 examples on page Advanced Math
Practice time 12-18 min
On-page examples 3 examples
Best for Advanced Math

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

If x/3 = 4, what is the value of x?

  1. 1
  2. 7
  3. 12
  4. 16
Show answer and explanation

Answer: 12

Multiply both sides by 3 to clear the denominator: x = 12.

Example 2 Medium

If 2/(x - 1) = 1, what is the value of x?

  1. 1
  2. 2
  3. 3
  4. 4
Show answer and explanation

Answer: 3

Multiply by x - 1 to get 2 = x - 1, so x = 3. This does not make the denominator zero.

Example 3 Hard

If 3/x = 1/(x - 2), what is the value of x?

  1. -3
  2. 0
  3. 2
  4. 3
Show answer and explanation

Answer: 3

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

Quick drills

Practice this skill from more angles

Drill 1

Identify values excluded by a denominator

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 2

Clear fractions using a common denominator

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 3

Solve equations containing rational expressions

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 4

Check that a solution is valid in the original equation

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

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

Related practice

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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.