Solving Rational Equations

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Solving Rational Equations
We will solve rational equations by using the LCD
to Get Rid of the Denominator!!!!
Domain (-8, 0)(0, 8)
LCD 2x
2
Check solution!
6 x 24 x 18 x 18
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Domain (-8, -1)(-1, 8)
LCD x 1
The whole point here is to CANCEL. Always cancel
before you multiply!!!!!
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5x 4x 4 5
5x 4x 1 x 1

1 is excluded from the domain
So, ?
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Domain (-8, -2)(-2, 2)(2, 8)
To find LCD, factor both denominators
x - 2 x - 2 x2 - 4 (x 2)(x -
2) LCD (x 2)(x - 2)
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Write denominators in factored form . . .
canceling is easier that way!!!
(3x 2)(x 2) 6 (x 2)(x 2)
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(3x 2)(x 2) 6 (x 2)(x 2)
3x2 4x 4 6 x2 4
2x2 4x 6 0
x2 2x 3 0
(x 3)(x 1) 0 x 3, 1
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Domain (-8, -4)(-4, 0)(0, 8)
Special case One fraction on each side use
cross multiplication!
(x2 4x)(1) 3(x4)
x2 4x 3x 12 x2 x 12 0 (x 4)(x 3)
0 x 4, 3
Look at domain!!!
x 3!!
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