SOLUTION: I cant seem to solve this equation.. PLease help :) x+2/x ------- = 5x 3+4/x Thank u :)

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Question 263102: I cant seem to solve this equation.. PLease help :)
x+2/x
------- = 5x
3+4/x
Thank u :)
Found 2 solutions by drk, josmiceli:
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%283%2B%284%2Fx%29%29+=+5x
step 1- multiply all terms by on the left by x to get
(ii) %28x%5E2+%2B+2%29%2F%283x%2B4%29+=+5x
step 2 - multiply both sides by (3x+4) to get
(iii) x%5E2+%2B+2+=+15x%5E2+%2B+20x
step 3 - set = 0 as
(iv) 14x%5E2+%2B20x+-2+=+0
by the quadratic, we get
x+=+%28-20+%2B-+sqrt%28400-4%2A14%2A%28-2%29%29%29%2F%2828%29
then
x+=+%28-20+%2B-+sqrt%28512%29%29%2F%2828%29
which simplifies to
x+=+%28-20+%2B-+16sqrt%282%29%29%2F%2828%29
and this reduces to
x+=+%28-5+%2B-+4sqrt%282%29%29%2F%287%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+%2B+2%2Fx%29%2F%283+%2B+4%2Fx%29+=+5x
Multiply both sides by 3+%2B+4%2Fx
x+%2B+2%2Fx+=+5x%2A%283+%2B+4%2Fx%29
x+%2B+2%2Fx+=+15x+%2B+20
Multiply both sides by x
x%5E2+%2B+2+=+15x%5E2+%2B+20x
14x%5E2+%2B+20x+-+2+=+0
7x%5E2+%2B+10x+-+1+=+0
Solve using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+7
b+=+10
c+=+-1
x+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A7%2A%28-1%29+%29%29%2F%282%2A7%29+
x+=+%28-10+%2B-+sqrt%28+100+%2B+28+%29%29%2F14+
x+=+%28-10+%2B+8%2Asqrt%282%29%29%2F14
(1) x+=+%28-5+%2B+4%2Asqrt%282%29%29%2F7
and
(2) x+=+%28-5+-+4%2Asqrt%282%29%29%2F7
You can check the 2 answers by plugging each back into equation