How Do You Solve a Rational Equation by LCD Multiplication?

How Do You Solve a Rational Equation by LCD Multiplication?

Note:

Want some extra practice solving rational equations? This tutorial gives you just that! You'll see how to solve a rational equation containing rational expressions with common denominators. Then, you'll see how to solve an equation containing rational expressions with unlike denominators. Take a look!

Keywords:

  • problem
  • rational
  • rational expression
  • variable
  • variables
  • fraction
  • algebraic fraction
  • fractions
  • similar denominator
  • same denominator
  • multiplication property of equality
  • least common denominator
  • lcd
  • excluded value
  • multiply by lcd

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

  • Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

      • How Do You Distribute With Whole Numbers and Fractions?How Do You Distribute With Whole Numbers and Fractions?

      How Do You Distribute With Whole Numbers and Fractions?

      This tutorial shows you how to distribute a whole number into the sum of fractions. It's an important skill to have when you're solving equations, and you never know when it can come up. Be sure to check out this tutorial!

  • Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

  • Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

      • How Do You Reduce Common Factors in a Rational Expression?How Do You Reduce Common Factors in a Rational Expression?

      How Do You Reduce Common Factors in a Rational Expression?

      Multiplying rational expressions? Want to cancel common factors out to make things easier to work with? In this tutorial, you'll see how to cancel out common factors in order to find the simplified product of two rational expression. Check it out!

Further Exploration

  • Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.