SOLUTION: 10/x - 12/x-3 + 4=0

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Question 44996: 10/x - 12/x-3 + 4=0
Answer by abhijitvakil(7) About Me  (Show Source):
You can put this solution on YOUR website!
multiply the entire equation by x(x-3). we get
x%28x-3%29%2A10%2Fx+-+x%28x-3%2912%2F%28x-3%29+%2B+x%28x-3%29%2A4+=+0
or
%28x-3%29%2A10+-12x+%2B+4x%5E2+-+12x+=+0
or
10x+-30+-12x+%2B+4x%5E2+-+12x+=+0
or
4x%5E2+-+14x+-+30+=+0
or
2x%5E2+-+7x+-15+=+0
this is the typical quadratic equation of type ax%5E2+%2B+bx+%2B+c+=+0, where
a = 2, b = -7 & c = -15.
The solution to this equation is provided by :
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29
substituting the values of a,b & c, we get the solution set or roots of this equation as:
x = (5, -3/2)