Free Algebra Tutorials!
 Home Miscellaneous Equations Operations with Fractions Undefined Rational Expressions Inequalities Writing Equations for Lines Using Sequences Intersections of Lines and Conics Graphing Linear Equations Solving Equations with Log Terms and Other Terms Quadratic Expresions - Complete Squares Adding and Subtracting Fractions with Like Denominators Multiplying a Fraction by a Whole Number Solving Equations with Log Terms and Other Terms Solving Quadratic Equations by Factoring Locating the Solutions of the Quadratic Equation Properties of Exponents Solving Equations with Log Terms on Each Side http: Graphs of Trigonometric Functions Estimating Products and Quotients of Mixed Numbers Inequalities The circle Adding Polynomials Adding Fractions with Unlike Denominators Factoring Polynomials Linear Equations Powers of Ten Straight Lines Dividing With Fractions Multiplication Property of Equality Rationalizing Denominators Multiplying And Dividing Fractions Distance Between Points on a Number Line Solving Proportions Using Cross Multiplication Using the Quadratic Formula Scientific Notation Imaginary Numbers Values of Symbols for Which Fractions are Undefined Graphing Equations in Three Variables Writing Fractions as Decimals Solving an Equation with Two Radical Terms Solving Linear Systems of Equations by Elimination Factoring Trinomials Positive Rational Exponents Adding and Subtracting Fractions Negative Integer Exponents Rise and Run Brackets Multiplying Square Roots Multiplying Polynomials Solving Systems of Linear Inequalities Multiplication Property of Radicals A Quadratic within a Quadratic Graphing a Linear Equation Calculations with Hundreds and Thousands Multiplication Property of Square and Cube  Roots Solving Equations with One Log Term The Cartesian Coordinate Plane Equivalent Fractions Adding and Subtracting Square Roots Solving Systems of Equations Exponent Laws Solving Quadratic Equations Factoring Trinomials Solving a System of Three Linear Equations by Elimination Factoring Expressions Adding and Subtracting Fractions The parabola Computations with Scientific Notation Quadratic Equations Finding the Greatest Common Factor Introduction to Fractions Simplifying Radical Expressions Containing One Term Polynomial Equations Graphing and Intercepts The Number Line Adding and Subtracting Rational Expressions with Different Denominators Scientific Notation vs Standard Notation Powers Factoring by Grouping Extraneous Roots Variables and Expressions Linera Equations Integers and Substitutions Squares and Square Roots Adding and Subtracting Rational Expressions with Different Denominators Solving Linear Inequalities Expansion of a Product of Binomials Powers and Exponents Finding The Greatest Common Factor Quadratic Functions The Intercepts of a Parabola Solving Equations Containing Rational Expressions http: Subtracting Polynomials Solving Equations Adding Fractions with Unlike Denominators Solving Systems of Equations by Substitution Solving Equations Product and Quotient of Functions
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Solving Equations Containing Rational Expressions

Example 1

Solve:

Solution

 Step 1 Find the LCD. LCD = 2 Â· 3 Â· x = 6x Step 2 Multiply by the LCD. Step 3 Distribute on the right side. Step 4 Reduce. Step 5 Solve. Simplify. Subtract 27 from both sides. Multiply both sides by -1. 18 = 27 - x-9 = -x 9 = x Step 6 Check the solution. We leave the check to you. Thus, the solution is x = 9.

Note:

Hereâ€™s one way to find the LCD of

â€¢ Factor each denominator:

x = x

2x = 2 Â· x

6 = 2 Â· 3

â€¢ List each factor the greatest number of times it appears in any factorization. x, 2, 3

â€¢ Multiply. 2 Â· 3 Â· x = 6x

So, the LCD is 6x.

Example 2

Solve:

Solution

 Step 1 Find the LCD. LCD = (x - 5)(x + 5) Step 2 Multiply by the LCD. Step 3 Distribute the LCD to both terms the right side. Step 4 Reduce. Step 5 Solve. Simplify. Distribute on the right side. Combine like terms. Add 5 to both sides. Divide both sides by 3. 16 16 16 21 7 = x + 5 + (x - 5) Â· 2 = x + 5 + 2x - 10 = 3x - 5 = 3x = x Step 6 Check the solution. We leave the check to you.
Thus, the solution is x = 7.
 All Right Reserved. Copyright 2005-2023