Question

What is the value of the expression $\frac{x-1}{x^{3/4}+x^{1/2}}\times \frac{x^{1/2}+x^{1/4}}{x^{1/2}+1}\times x^{1/4}$, when x = 16 ?

Answer 1

$\frac{16-1}{{16}^{\frac{3}{4}}+{16}^{\frac{1}{2}}}\times \frac{{16}^{\frac{1}{2}}+{16}^{\frac{1}{4}}}{{16}^{\frac{1}{2}}+1}\times {16}^{\frac{1}{4}}$

$=\frac{15}{(2^4{)}^{\frac{3}{4}}+(4^2{)}^{\frac{1}{2}}}\times \frac{(4^2{)}^{\frac{1}{2}}+(2^4{)}^{\frac{1}{4}}}{(4^2{)}^{\frac{1}{2}}+1}\times (2^4{)}^{\frac{1}{4}}$

$=\frac{15}{2^3+4}\times \frac{4+2}{4+1}\times 2$

$=\frac{15}{12}\times \frac{6}{5}\times 2=3$