SOLUTION: 2/x-1 + 6/x+1 = 7x/x^2-1 what is the solution for x=

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Question 477856: 2/x-1 + 6/x+1 = 7x/x^2-1
what is the solution for x=
Answer by Maths68(1474) About Me  (Show Source):
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2/x-1 + 6/x+1 = 7x/x^2-1
2/x-1 + 6/x+1 = 7x/(x^2-1^2) because 1^2=1
Taking LCM on left hand side and expand x^2-1^ on right hand side
[2(x+1)+6(x-1)]/[(x-1)(x+1)]=7x/[(x-1)(x+1)] because (a^2-b^2)=(a-b)(a+b)
[2(x+1)+6(x-1)]/[(x-1)(x+1)]=7x/[(x-1)(x+1)]
[(2x+2+6x-6/)]/[(x-1)(x+1)]= 7x/[(x-1)(x+1)]
Multiply by (x-1)(x+1) both sides
2x+2+6x-6= 7x
8x-4= 7x
Substract -7x from both sides
8x-4-7x= 7x-7x
x-4=0
x=4
Check:
2/x-1 + 6/x+1 = 7x/x^2-1
Put x=4
2/(4-1)+6(4+1)=[7(4)]/[(4)^2-1]
2/3+6/5=28/[16-1)
Taking LCM
[(2*5)+(6*3)]/15=28/15
[10+18]/15=28/15
28/15=28/15