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Rational expressions practice

Solving rational equations worksheets

Practice ten exact rational equations with monomial or binomial expressions, original-domain restrictions and checked rational solutions.

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Solve each equation. Keep the original denominators nonzero and reject excluded solutions.

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A4

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Check every solution in the original equation

Each worksheet contains ten equations. Choose monomial expressions, expressions containing binomials or a balanced mix; the seed keeps the selected family schedule reproducible.

The answer key gives the exact solution set and prints every variable-bearing original denominator condition. Candidates are checked against the original domain and substituted into the original equation.

Learning objective

What this activity builds

Solve a rational equation exactly, keep every original denominator nonzero and reject any candidate excluded by the original equation.

Worked example

Solve 1/x + (3x + 12)/(x² − 6x) = (10x − 20)/(x² − 6x).

x = 13/3, with x ≠ 0 and x − 6 ≠ 0.

Record the original restrictions, multiply through by a product of the denominators, solve the resulting equation and substitute the candidate into the original equation.

Teaching notes

Make the practice count

  • Write every original denominator restriction before clearing fractions.
  • Multiply every term by a common denominator product and collect the residual exactly.
  • Solve the resulting linear or quadratic equation.
  • Check each candidate in the original equation and reject excluded values.

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Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose monomial expressions, expressions containing binomials or both, then change the seed for a reproducible set of ten equations.

Worksheet settings

Expression types

Monomial practice uses single-term components. Binomial practice includes at least one two-term numerator or denominator in every equation.

Page note and reproducible seed

The same settings and seed make the same questions. Shared links include your page note; leave personal information out. Notes use the selected language’s supported characters; English accepts basic Latin text.

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Math SheetNameScore/ 10TeacherDateSolving Rational EquationsSolve each equation. Keep the original denominators nonzero and reject excluded solutions.1.124s2=112s2+1s2.s+120s2+510s2=s-310s23.1q2=11214.1c+6c+4c2-3c=11c+2c2-3c5.1x+12x-2x2-5x=10x+3x2-5x6.1c=8c+107.1c2=1648.p-416p2+108p2=p+108p29.y-42y2+8y2=y-4y210.1s=712s-9math-sheet.comPage 1 / 1

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