What is the value of the expression (x-1)/(x^(3/4))+ (x^(1/2).x^(1/2)+x^(1/4))/(x^(1/2)+1). x^(1/4) when x = 16 ?

Question

What is the value of the expression \(\frac{x-1}{x^{\frac34}+x^{\frac12}}. \frac{x^{\frac12}+x^{\frac14}}{x^{\frac12}+1}.x^{\frac14}\) when x = 16?

Answer 1

Required value =

= \(\frac{15}{2^3+4}.\frac{4+2}{4+1}.2 = \frac{15}{12}\times\frac65\times2=3.\)