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Solving Rational Equations: Procedure and Examples, Exercises of Calculus

Silliman University (SU)Calculus

An introduction to rational equations, explaining the steps to solve them, and includes exercises for practice. Students will learn how to factor denominators, identify restricted values, find the LCD, and clear fractions to solve the resulting equation.

Typology: Exercises

2021/2022

Uploaded on 08/05/2022

hal_s95
hal_s95 🇵🇭

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Rational Equations
Introduction to Rational Equations
Definition: An equation with one or more rational expressions is called a rational equation.
Note: We can clear the fractions in an equation by multiplying both sides of the equation by the LCD of all terms.
For exercises 1 and 2, solve the equations by first clearing the fractions.
1. 2.
Solving Rational Equations
PROCEDURE Solving a Rational Equation
Step 1 Factor the denominators of all rational expressions. Identify the restricted values.
Step 2 Identify the LCD of all expressions in the equation.
Step 3 Multiply both sides of the equation by the LCD.
Step 4 Solve the resulting equation.
Step 5 Check potential solutions in the original equation
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Rational Equations Introduction to Rational Equations Definition: An equation with one or more rational expressions is called a rational equation. Note : We can clear the fractions in an equation by multiplying both sides of the equation by the LCD of all terms. For exercises 1 and 2, solve the equations by first clearing the fractions.

Solving Rational Equations PROCEDURE Solving a Rational Equation Step 1 Factor the denominators of all rational expressions. Identify the restricted values. Step 2 Identify the LCD of all expressions in the equation. Step 3 Multiply both sides of the equation by the LCD. Step 4 Solve the resulting equation. Step 5 Check potential solutions in the original equation

  1. For the equation a. Identify the restricted values. b. Identify the LCD of the fractions in the equation. c. Solve the equation. For exercises 4 – 9 , solve the equations.

For exercises 10 and 11, translate to a rational equation and solve.

  1. Three times a number divided by the sum of the number and four is equal to 5. Find the number.
  2. Three times the reciprocal of a number is subtracted from five. The result is the quotient of seven and the number. Find the number.

Solving Formulas Involving Rational Expressions For exercises 12 – 16 , solve for the indicated variable.

  1. for V 13. for
  2. for p 15. for a
  3. for x