Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.40

Pre CAL.40 Solving Rational Equations and Inequalities Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.40 Solving Rational Equations and Inequalities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.40 Solving Rational Equations and Inequalities - Solving Rational Equations and Inequalities

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

Pre-Calculus

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 Pre CAL.40 Solving Rational Equations and Inequalities skill assessments:

Problem 1Difficulty: Mastery

Solve the inequality: (x squared - 4) over (x squared - 4x) >= 0. Choose the solution set.

A(-infinity, -2) U (0, 2) U (4, infinity)

B(-infinity, -2] U (0, 4)

C(-infinity, -2] U (0, 2] U (4, infinity)

D(-infinity, 0) U (2, 4)

Solution & Explanation:Factor: (x-2)(x+2) over x(x-4). Restrictions: x!= 0 and x!= 4. Sign chart at -2,0,2,4 gives >=0 on (-infinity,-2], (0,2], and (4,infinity).

Problem 2Difficulty: Mastery

Solve for x: (x + 1) over (x - 2) = (x - 2) over (x + 1) + 1. Choose the solution set.

A{(7 - 3sqrt(5)) over 2}

B{(7 - 3sqrt(5)) over 2, (7 + 3sqrt(5)) over 2}

C{(7 + 3sqrt(5)) over 2}

Dno solution

Solution & Explanation:Restrictions: x!= 2 and x!= -1. Multiply by (x-2)(x+1) and simplify to the quadratic x squared -7x +1 = 0. Quadratic formula gives x = (7 + over - 3sqrt(5)) over 2. Both satisfy restrictions.

Problem 3Difficulty: Mastery

Solve the inequality: (x squared - 6x + 8) over (x squared - 4x + 4) >= 0. Choose the solution set.

A(-infinity, 2) U [4, infinity)

B(-infinity, 2) U (2, 4)

C[2, 4]

D(-infinity, 4]

Solution & Explanation:Factor to (x-2)(x-4) over (x-2) squared. For x!=2 it behaves like (x-4) over (x-2), but x=2 is excluded. A sign chart shows it is >=0 for x<2 and x>=4. So (-infinity,2) U [4,infinity).

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this Pre CAL.40 Solving Rational Equations and Inequalities worksheet?

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QIs this Pre CAL.40 Solving Rational Equations and Inequalities worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard Pre-CAL.40 (Solving Rational Equations and Inequalities).