Question

Solve:
${(x+1-\frac{1}{x})}^3$

Answer 1

${(x+1-\frac{1}{x})}^3$

$=\frac{{(x^2+x-1)}^3}{x^3}$

$=\frac{{(x^2+x)}^3-1-3(x^2+x)(x^2+x-1)}{x^3}(\because {(a-b)}^3=a^3-b^3-3ab(a-b))$

$=\frac{{(x^2+x)}^3-1-3{(x^2+x)}^2+3(x^2+x)}{x^3}$

$=\frac{x^6+x^3+3x^3(x^2+x)-1-3(x^4+x^2+2x^3)+3x^2+3x}{x^3}$

$=\frac{x^6+x^3+3x^5+3x^4-1-3x^4-3x^2-6x^3+3x^2+3x}{x^3}$

$=\frac{x^6+3x^5-5x^3+3x-1}{x^3}$