Prove that `(2^(log_(2^(1//4))x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)gt0,AAx in(0,oo)`.

Prove that `(2^(log_(2^(1//4))x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4lo

1.	Prove that `(2^(log_(2^(1//4))x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)gt0,AAx in(0,oo)`.
Answer» `(2^(log2^(1//4)x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)` `=(2^(log_(2)x^(4))-3^(log_(3)(x^(2)+1))-2x)/(7^(log_(7)x^(2))-x-1)` `(x^(2)-(x^(2)+2x+1))/(x^(2)-x-1)` `=x^(2)+x+1` `(x+(1)/(2))^(2)+(3)/(4)gt0,AAx inR`