Solve the equation. Check all proposed solutions. Show work in solving and in checking.

x + x = 102

x-3 x+3 x^2-9

Solve the equation. Check all proposed solutions. Show work in solving and in checking.

x + x = 102

x-3 x+3 x^2-9

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Olney, MD

First let's add the fractions on the left. To add any fraction, you must put them over a common denominator, in this case (x-3)(x+3)

x (x+3) x (x-3)

------ ------ + ------ -------

(x-3) (x+3) (x+3) (x-3)

Multiply out the numerator and denominator then combine like terms

x^{2} + 3x + x^{2} - 3x 2x^{2}

--------------------- = ------

x^{2} - 9 x^{2}-9

--------------------- = ------

x

Now we can re-state the original problem as:

2x^{2}/(x^{2}-9) = 102/(x^{2}-9)

2x^{2} = 102 (Multiply both sides by (x^{2}-9) )

x^{2} = 51 (Divide both sides by 2)

x = ±√51 (Take the square root of both sides)

To check, plug x = +√51 and x = -√51 into your original equation (below) and make sure the left hand side equals the right hand side. If it does, it's a solution.

2x^{2}/(x^{2}-9) = 102/(x^{2}-9)

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