SOLUTION: In Solving Equations with Rational Expressions how do I answer this problem: x/2 - 2/3 = 1/x? I figured out this: x/3-2/3 = 1/x, x-2/3 = 1/x, then I cross multiply and I would be

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: In Solving Equations with Rational Expressions how do I answer this problem: x/2 - 2/3 = 1/x? I figured out this: x/3-2/3 = 1/x, x-2/3 = 1/x, then I cross multiply and I would be       Log On


   

Question 32574: In Solving Equations with Rational Expressions how do I answer this problem:
x/2 - 2/3 = 1/x? I figured out this: x/3-2/3 = 1/x, x-2/3 = 1/x, then I cross multiply and I would be at x^2-2x = 3 but after that I'm stuck.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
x%2F2+-+2%2F3+=+1%2Fx Simplify the left side.
%283x-4%29%2F6+=+1%2Fx Multiply both sides by 6.
3x-4+=+6%2Fx Multiply both sides by x.
3x%5E2-4x+=+6 Subtract 6 from both sides.
3x%5E2-4x-6+=+0 Solve this using the quadratic formula:x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a.
x+=+%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%281%29%28-6%29%29%29%2F2%281%29
x+=+%284%2B-sqrt%2816%2B24%29%29%2F2
x+=+%284%2B-sqrt%2840%29%29%2F2
x+=+%284%2B-2sqrt%2810%29%29%2F2
x+=+2%2Bsqrt%2810%29 or x+=+2-sqrt%2810%29