SOLUTION: To solve the rational equation below, which step would result? 3/x+1/2= 8/(x+2) I got: 3(x+2) + .5 = 8X Is this correct? Thanks~

Question 78391: To solve the rational equation below, which step would result?
3/x+1/2= 8/(x+2)
I got: 3(x+2) + .5 = 8X
Is this correct?
Thanks~

Answer by dolly(163) (Show Source): You can put this solution on YOUR website!
3/x + 1/2 = 8/(x+2)
On multiplying by the LCD this would result in,
3(x+2) + 0.5 x(x+2) = 8x
==> 3x + 6 + 0.5x^2 + x = 8x
==> 0.5x^2 + 4x + 6 = 8x
Adding - 8x to both the sides,
==> 0.5x^2 -4x + 6 = 0
==> 5x^2 - 40x + 60 = 0 [multiplying by 10]
==> x^2 - 8x + 12 = 0 [dividing by 5]
==> x^2 - 6x - 2x + 12 = 0
==> x(x-6) - 2(x-6) = 0
==> (x-6)(x-2) = 0
==> x-6 = 0 or x-2= 0
==> x = 6 or x= 2

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