SOLUTION: (x+(2/x))/(7-(2/x))=6x

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Question 262817: (x+(2/x))/(7-(2/x))=6x
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original problem:
(i) %28x%2B%282%2Fx%29%29%2F%287-%282%2Fx%29%29=6x
step 1 - cross multiply to get
(ii) x%2B+%282%2Fx%29+=+42x+-12
step 2 - multiply by x to get
(iii) x%5E2+%2B+2+=+42x%5E2+-+12x
step 3 - set = 0 to get
(iv) 0+=+41x%5E2+-+12x+-+2
step 4 - by the quadratic, we get
x+=+%2812+%2B-+sqrt%28+144-4%2A41%2A%28-2%29+%29%29%2F%2882%29+
which is
x+=+%2812+%2B-+sqrt%28+472%29%29%2F%2882%29+
and then
x+=+%2812+%2B-+2sqrt%28+118%29%29%2F%2882%29+
and reducing, we get
x+=+%286+%2B-+sqrt%28+118%29%29%2F%2841%29+