Free Printable WorksheetMathAlgebra IMath CurriculumA-APR.1 (coherence)

ALG1.99 Solve Rational Equations and Check for Extraneous Solutions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.99 Solve Rational Equations and Check for Extraneous Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.99 Solve Rational Equations and Check for Extraneous Solutions - Select the correct solution to rational equations and check solutions against excluded values; Select the statement that correctly interprets extraneous solutions as artifacts of multiplying by expressions that can be zero. (CCSS: A-APR.1 (coherence); TEKS: §111.39(c)(10)(C)–(D); VA SOL: A.EO.2 d; FL B.E.S.T.: MA.912.AR.1.4; NY-NGLS: AI-A.SSE.2 (rewriting) connections; CA CCSSM: A-APR connections; MA 2017: HS.A-APR.1 (course model dependent); DoDEA CCRSM; NAEP: Algebra—symbolic manipulation; NCTM P2A: Practices 6, 7.)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG1.99 Solve Rational Equations and Check for Extraneous Solutions skill assessments:

Problem 1Difficulty: Mastery

A student multiplies both sides of a rational equation by (x - 2)(x + 7). What is the most important domain note before accepting answers?

Ax = 2 and x = -7 cannot be solutions if they made original denominators 0

Bx = -2 and x = 7 cannot be solutions

CEvery candidate from the cleared equation is automatically valid

DOnly integer candidates can be valid

Solution & Explanation:The product (x - 2)(x + 7) can be 0 at x = 2 and x = -7. Those values must be excluded if they make original denominators 0.

Problem 2Difficulty: Mastery

Which pair of checks is necessary after solving 5/(x - 4) = 10/(x + 1)?

ACheck x = 4 and x = -1 as excluded values, then test the candidate in the original equation

BCheck only whether the candidate is positive

CCheck whether the numerators are equal

DCheck x = 5 and x = 10 because they are numerators

Solution & Explanation:The denominators x - 4 and x + 1 exclude x = 4 and x = -1. After solving the cleared equation, the candidate must be tested against those exclusions and the original equation.

Problem 3Difficulty: Mastery

A calculator solves a cleared equation and returns x = 5 for (x - 5)/(x - 5) = 0. Which explanation should be used?

AReject x = 5; the original expression is undefined there and no allowed x makes 1 = 0

BAccept x = 5; calculators cannot create extraneous solutions

CAll real numbers except x = 5 solve the equation

DAccept all real numbers because the factor cancels

Solution & Explanation:The original expression is undefined at x = 5. For all allowed x, (x - 5)/(x - 5) equals 1, not 0, so there is no solution.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-APR.1 (coherence) (Students solve rational equations, identify excluded values, check candidate solutions in the original equation, and explain extraneous solutions created by multiplying by expressions that may be zero. Associated standards include CCSS A-APR.1 for algebraic coherence, with related state and local rational-expression standards as applicable.).