2.6. Solving Rational Equations http://www.ck12.org
2.6 Solving Rational Equations
Here you will extend your knowledge of linear and quadratic equations to rational equations in general. You will
gain insight as to what extraneous solutions are and how to identify them.
The techniques for solving rational equations are extensions of techniques you already know. Recall that when
there are fractions in an equation you can multiply through by the denominator to clear the fraction. The same
technique helps turn rational expressions into polynomials that you already know how to solve. When you multiply
by a constant there is no problem, but when you multiply through by a value that varies and could possibly be zero
interesting things happen.
Since every equation is trivially true when both sides are multiplied by zero, how do you account for this when
solving rational equations?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/60820http://www.youtube.com/watch?v=MMORnvhR4wA James Sousa: Solving Rational Equations
Guidance
The first step in solving rational equations is to transform the equation into a polynomial equation. This is
accomplished by clearing the fraction which means multiplying the entire equation by the common denominator
of all the rational expressions. Then you should solve using what you already know. The last thing to check once
you have the solutions is that they do not make the denominators of any part of the equation equal to zero when
substituted back into the original equation. If so, that solution is calledextraneousand is a “fake” solution that was
introduced when both sides of the equation were multiplied by a number that happened to be zero.
Example A
Solve the following rational equation.
x−x+^53 = 12
Solution:Multiply all parts of the equation by(x+ 3 ), the common denominator.