Question

Solve:$\frac{1-x\sqrt{x}}{1+x\sqrt{x}}$

Answer 1

Given, $\frac{1-x\sqrt{x}}{1+x\sqrt{x}}$

Multiplying the numerator and denominator by $1-x\sqrt{x}$ we get,

$\frac{(1-x\sqrt{x})(1-x\sqrt{x})}{(1+x\sqrt{x})(1-x\sqrt{x})}=\frac{{(1-x\sqrt{x})}^2}{1^2-{\left(x\sqrt{x}\right)}^2}=\frac{1^2-2x\sqrt{x}+{\left(x\sqrt{x}\right)}^2}{1-x^3}=\frac{1-2x\sqrt{x}+x^3}{1-x^3}.$