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ALG2.125 Simplifying Rational Expressions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.125 Simplifying Rational Expressions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.125 Simplifying Rational Expressions - Practice questions for Simplifying Rational Expressions.

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Grade

Algebra II

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 ALG2.125 Simplifying Rational Expressions skill assessments:

Problem 1Difficulty: Mastery

Simplify and list all values of x that are not allowed: ((3x² - 30x + 27) ÷ (x² - 8x + 7)) ÷ (((2x³ + 4x² - 58x + 84) ÷ (x + 7)) ÷ ((x² - 7x - 18) ÷ (x + 2)))

A(6x² - 30x + 36) ÷ (x - 7); excluded values: x ≠ -7, x ≠ -2, x ≠ 1, x ≠ 2, x ≠ 3, x ≠ 7, x ≠ 9

B(2x³ - 24x² + 82x - 84) ÷ (3x² - 54x + 243); excluded values: x ≠ -7, x ≠ -2, x ≠ 1, x ≠ 2, x ≠ 3, x ≠ 7, x ≠ 9

C(3x² - 54x + 243) ÷ (2x³ - 24x² + 82x - 84); excluded values: x ≠ -7, x ≠ -2, x ≠ 1, x ≠ 7

D(3x² - 54x + 243) ÷ (2x³ - 24x² + 82x - 84); excluded values: x ≠ -7, x ≠ -2, x ≠ 1, x ≠ 2, x ≠ 3, x ≠ 7, x ≠ 9

Solution & Explanation:Find excluded values first: any x that makes a denominator 0 is not allowed, and if you divide by an expression, that divisor must not be 0. Excluded values: x ≠ -7, x ≠ -2, x ≠ 1, x ≠ 2, x ≠ 3, x ≠ 7, x ≠ 9. Factor each polynomial: 3x² - 30x + 27 = 3(x - 1)(x - 9) x² - 8x + 7 = (x - 1)(x - 7) 2x³ + 4x² - 58x + 84 = 2(x + 7)(x - 2)(x - 3) x + 7 = (x + 7) x² - 7x - 18 = (x + 2)(x - 9) x + 2 = (x + 2) Rewrite division as multiplication by the reciprocal of the divisor, then cancel common factors. Simplified result: (3x² - 54x + 243) ÷ (2x³ - 24x² + 82x - 84).

Problem 2Difficulty: Mastery

Choose the correct simplification and complete set of excluded values: ((x² - 17x + 72) ÷ (x³ - 9x² - 16x + 144)) ÷ (((2x² + 30x + 108) ÷ (x + 6)) ÷ ((2x² + 2x - 12) ÷ (x + 3)))

A(x² + x - 72) ÷ (x³ - 2x² - 16x + 32); excluded values: x ≠ -9, x ≠ -6, x ≠ -4, x ≠ -3, x ≠ 2, x ≠ 4, x ≠ 9

B(x³ + 9x² - 16x - 144) ÷ (x² - 10x + 16); excluded values: x ≠ -9, x ≠ -6, x ≠ -4, x ≠ -3, x ≠ 2, x ≠ 4, x ≠ 9

C(x² - 10x + 16) ÷ (x³ + 9x² - 16x - 144); excluded values: x ≠ -9, x ≠ -6, x ≠ -4, x ≠ -3, x ≠ 2, x ≠ 4, x ≠ 9

D(x² - 10x + 16) ÷ (x³ + 9x² - 16x - 144); excluded values: x ≠ -6, x ≠ -4, x ≠ -3, x ≠ 4, x ≠ 9

Solution & Explanation:Find excluded values first: any x that makes a denominator 0 is not allowed, and if you divide by an expression, that divisor must not be 0. Excluded values: x ≠ -9, x ≠ -6, x ≠ -4, x ≠ -3, x ≠ 2, x ≠ 4, x ≠ 9. Factor each polynomial: x² - 17x + 72 = (x - 9)(x - 8) x³ - 9x² - 16x + 144 = (x - 9)(x - 4)(x + 4) 2x² + 30x + 108 = 2(x + 6)(x + 9) x + 6 = (x + 6) 2x² + 2x - 12 = 2(x + 3)(x - 2) x + 3 = (x + 3) Rewrite division as multiplication by the reciprocal of the divisor, then cancel common factors. Simplified result: (x² - 10x + 16) ÷ (x³ + 9x² - 16x - 144).

Problem 3Difficulty: Mastery

Rewrite the division as multiplication by a reciprocal, then simplify and state excluded values: (((x² - 8x + 12) ÷ (x² - 15x + 54)) ÷ ((x² - 16) ÷ (x² + 3x - 28))) ÷ ((2x² - 16x + 30) ÷ (x² - 25))

A(2x³ + 4x² - 58x + 84) ÷ (x³ - 61x - 180); excluded values: x ≠ -7, x ≠ -5, x ≠ -4, x ≠ 3, x ≠ 4, x ≠ 5, x ≠ 6, x ≠ 9

B(x³ + 10x² + 11x - 70) ÷ (2x³ - 16x² - 42x + 216); excluded values: x ≠ -7, x ≠ -5, x ≠ -4, x ≠ 3, x ≠ 4, x ≠ 5, x ≠ 6, x ≠ 9

C(2x³ - 16x² - 42x + 216) ÷ (x³ + 10x² + 11x - 70); excluded values: x ≠ -7, x ≠ -5, x ≠ -4, x ≠ 3, x ≠ 4, x ≠ 5, x ≠ 6, x ≠ 9

D(x³ + 10x² + 11x - 70) ÷ (2x³ - 16x² - 42x + 216); excluded values: x ≠ -7, x ≠ -5, x ≠ 4, x ≠ 5, x ≠ 6, x ≠ 9

Solution & Explanation:Find excluded values first: any x that makes a denominator 0 is not allowed, and if you divide by an expression, that divisor must not be 0. Excluded values: x ≠ -7, x ≠ -5, x ≠ -4, x ≠ 3, x ≠ 4, x ≠ 5, x ≠ 6, x ≠ 9. Factor each polynomial: x² - 8x + 12 = (x - 6)(x - 2) x² - 15x + 54 = (x - 9)(x - 6) x² - 16 = (x - 4)(x + 4) x² + 3x - 28 = (x + 7)(x - 4) 2x² - 16x + 30 = 2(x - 5)(x - 3) x² - 25 = (x + 5)(x - 5) Rewrite division as multiplication by the reciprocal of the divisor, then cancel common factors. Simplified result: (x³ + 10x² + 11x - 70) ÷ (2x³ - 16x² - 42x + 216).

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard ALG2.125 (Practice questions for Simplifying Rational Expressions.).