SOLUTION: Solve and check each of the following equations for x. Please help me. Thank you

Question 29621: Solve and check each of the following equations for x.

Please help me.
Thank you
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
x/(x-2) - (x+1)/x = 8/(x^2-2x) ----(1)
x/(x-2) - (x+1)/x = 8/x(x-2)
Multiply by x(x-2) through out
xX(x)-(x+1)(x-2) = 8
x^2-[x(x-2)+1(x-2)]= 8
x^2-[x^2-2x+x-2] = 8
x^2-x^2+2x-x+2 = 8
(x^2-x^2)+(2x-x) = 8-2 (grouping like terms)
0+x = 6
x=6
Answer: x = 6
Verification: Putting x= 6 in (1) we have LHS = 1/3 =RHS
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