SOLUTION: (1/x)-(1/x+1)=3

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Question 657012: (1/x)-(1/x+1)=3
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+-+1%2F%28x%2B1%29+=+3

%28x%2B1%29%2F%28x%5E2+%2B+x%29+-+x%2F%28x%5E2+%2B+x%29+=+3
%28x+%2B+1+-+x%29+%2F+%28x%5E2+%2B+x%29+=+3
1%2F%28x%5E2+%2B+x%29+=+3
%28x%5E2%2Bx%29%2A%281%2F%28x%5E2%2Bx%29%29+=+3%2A%28x%5E2%2Bx%29
1+=+3%2Ax%5E2+%2B+3%2Ax
3%2Ax%5E2+%2B+3%2Ax+-+1+=+3
We can solve for x using the quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ with x=3, b=3, and c=-1
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A3%2A%28-1%29+%29%29%2F%282%2A3%29+
x+=+%28-3+%2B-+sqrt%28+9%2B12+%29%29%2F6+
x+=+%28-3+%2B-+sqrt%28+21+%29%29%2F6+
So x = -1.264 or x = 0.264 (rounded to three decimal places).
1%2F%28-1.264%29+-+1%2F%28-1.264%2B1%29+=+-0.179+-+-3.179+=+3
1%2F0.264+-+1%2F%280.264%2B1%29+=+3.179+-+0.791+=+3