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# ​Solving Rational Equations

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Solve this rational equation.

$${2 \over x-3} - {4 \over x+3} = {8 \over x^2-9}$$

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Solve for x:
2/(x - 3) - 4/(x + 3) = 8/(x^2 - 9)

Look for a polynomial to multiply both sides by in order to clear fractions.
Multiply both sides by x^2 - 9:
2 (x + 3) - 4 (x - 3) = 8

Write the linear polynomial on the left-hand side in standard form.
Expand out terms of the left-hand side:
18 - 2 x = 8

Isolate terms with x to the left-hand side.
Subtract 18 from both sides:
-2 x = -10

Solve for x.
Divide both sides by -2:

x = 5

Guest Sep 12, 2017