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Simplifying Rational Expressions - Worksheet 6 - 11th Grade

Medium

Simplify rational expressions, solve rational equations and retain excluded domain values.

medium: Practice the same exercise types with a fresh numbered set.

24 problems · 20-25 minutes · Skills: rational expressions, simplification, factoring

About This Worksheet

This medium-level worksheet contains 24 problems designed for 11th Grade students practicing simplifying rational expressions. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Factor polynomials, use exponent laws and solve equations with domain restrictions.

  • Simplify rational expressions, solve rational equations and retain excluded domain values.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Simplify (x² − 16)/(x − 4). State the excluded value from the original expression.
Solution Steps:
  1. Factor the numerator as a difference of squares.
  2. Cancel the common factor where it is nonzero.
  3. Keep the original denominator restriction.
Answer: x + 4; x ≠ 4
Tip: Check your result using the method in the example before moving to the next question.
1
Simplify (x² − 4)/(x − 2). State the excluded value from the original expression.
2
Simplify (x² − 64)/(x − 8). State the excluded value from the original expression.
3
Simplify (x² − 16)/(x − 4). State the excluded value from the original expression.
4
Simplify (x² − 9)/(x − 3). State the excluded value from the original expression.
5
Simplify (x² − 36)/(x − 6). State the excluded value from the original expression.
6
Simplify (x² − 49)/(x − 7). State the excluded value from the original expression.
7
Simplify (x² − 1)/(x − 1). State the excluded value from the original expression.
8
Simplify (x² − 25)/(x − 5). State the excluded value from the original expression.
9
Simplify (x² − 64)/(x − 8). State the excluded value from the original expression.
10
Simplify (x² − 1)/(x − 1). State the excluded value from the original expression.
11
Simplify (x² − 49)/(x − 7). State the excluded value from the original expression.
12
Simplify (x² − 25)/(x − 5). State the excluded value from the original expression.
13
Simplify (x² − 9)/(x − 3). State the excluded value from the original expression.
14
Simplify (x² − 4)/(x − 2). State the excluded value from the original expression.
15
Simplify (x² − 1)/(x − 1). State the excluded value from the original expression.
16
Simplify (x² − 64)/(x − 8). State the excluded value from the original expression.
17
Simplify (x² − 49)/(x − 7). State the excluded value from the original expression.
18
Simplify (x² − 16)/(x − 4). State the excluded value from the original expression.
19
Simplify (x² − 1)/(x − 1). State the excluded value from the original expression.
20
Simplify (x² − 64)/(x − 8). State the excluded value from the original expression.
21
Simplify (x² − 4)/(x − 2). State the excluded value from the original expression.
22
Simplify (x² − 9)/(x − 3). State the excluded value from the original expression.
23
Simplify (x² − 49)/(x − 7). State the excluded value from the original expression.
24
Simplify (x² − 16)/(x − 4). State the excluded value from the original expression.

Answer Key

1. x + 2; x ≠ 22. x + 8; x ≠ 83. x + 4; x ≠ 44. x + 3; x ≠ 35. x + 6; x ≠ 66. x + 7; x ≠ 77. x + 1; x ≠ 18. x + 5; x ≠ 59. x + 8; x ≠ 810. x + 1; x ≠ 111. x + 7; x ≠ 712. x + 5; x ≠ 513. x + 3; x ≠ 314. x + 2; x ≠ 215. x + 1; x ≠ 116. x + 8; x ≠ 817. x + 7; x ≠ 718. x + 4; x ≠ 419. x + 1; x ≠ 120. x + 8; x ≠ 821. x + 2; x ≠ 222. x + 3; x ≠ 323. x + 7; x ≠ 724. x + 4; x ≠ 4

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What skills does this rational functions worksheet cover?

This worksheet focuses on rational expressions, simplification, factoring. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 24 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.