Rational Equations with Extraneous Solutions Lesson Slides

8 Slides • 2 Questions

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6.4 Part III - Solve Rational Equations

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Rational Equation

A rational equation is an equation that contains one or more rational expressions.

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Let's think back to when we learned how to add fractions

We need a common denominator, right?
$\frac{1}{2}+\frac{1}{3}=?$
What is the LCM of 2 & 3? Six, right? So our common denominator is 6.
So we multiply the top and bottom of both fractions by the "missing factor". $\frac{1\cdot3}{2\cdot3}+\frac{1\cdot2}{3\cdot2}=\frac{3+2}{6}=\frac{5}{6}$

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Example

$\frac{6}{x}+\frac{5}{4}=-\frac{7}{4}$
We have an x and a 4 for denominators, so our LCM is 4*x = 4x
$\frac{6\cdot4}{x\cdot4}+\frac{5\cdot x}{4\cdot x}=-\frac{7\cdot x}{4\cdot x}$
$\frac{24}{4x}+\frac{5x}{4x}=-\frac{7x}{4x}$
$24+5x=-7x$
$24=-12x$
$-2=x$

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Recall that we have to test for extraneous solutions.

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7

Multiple Choice

Solve the rational equation $\frac{16}{x^2-16}=\frac{2}{x-4}$

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$x=-4;\ x=4\ is\ an\ extraneous\ solution$

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There are no solutions because $x=4$ is an extraneous solution

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There are no solutions because $x=16$ is an extraneous solution

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$x=4,\ x=\ -4$

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You try

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Open Ended

Solve the rational equation $4=\frac{3}{2-c}+\frac{3}{2+c}$

Type response here

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Some quick practice on MathXL and you're good to go for the day.

6.4 Part III - Solve Rational Equations

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