Prove that `(2^((log)_2 1/4x)-3^(log)_(27)(x^2+1)^3-2x >)/(7^(4(log)_(49)x)-x-1)0`

Explanation

`(2^(log_2^(1/4x))-3^(log_2^(x^2+1)^3)-2x)/(7^(4log_49^x)-x-1)>0`

`(2^(log_2^(x)^4)-3^(log_3^(x^2+1))-2x)/(7^(log_1^(sqrtx)^4)-x-1)`

`(x^4-(x^2+1)-2x)/(x^2-x-1)>0`

`(x^4-(x^2+2x+1))/(x^2-x-1)>0`

`((x^2)^2-(x+1)^2)/(x^2-x-1)>0`

`((x^2+x+1)(x^2-x-1))/(x^2-x-1)>0`

`x^2+x+1>0`

`(x+1/2)^2+3/4>0`

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