Solving Rational Equations

1.  To solve simple rational equations, you can use cross multiplication.  You can also multiply both sides by the LCM of the two denominators.  Shown below, cross multiplication is used to solve.

1. \(\dfrac{x-1}{5}=\dfrac{9}{7}\)
2. \(\dfrac{x+2}{3}=\dfrac{4}{9}\)

2. What about more complicated equations?

Try finding common denominators as a first step in solving the next equations. Once all of the terms have a common denominator, solve the equation created by the numerators.

1. \(\dfrac{3}{x+4}+\dfrac{1}{4}= 5\)
2. \(\dfrac{x}{x-5}+\dfrac{3}{x+2}=\dfrac{7x}{x^2-3x-10}\)

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Check solutions here.

Go to Making Connections (Solving Rational Equations)