What is expand (x(x+1)+1)/x ?

The solution to expand (x(x+1)+1)/x is x+1+1/x

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expand (x(x+1)+1)/x

expand

\frac{x ( x + 1 ) + 1}{x}

x + 1 + \frac{1}{x}

Solution steps

\frac{x ( x + 1 ) + 1}{x}

Expand

x (x + 1) + 1 : x^{2} + x + 1

= \frac{x ^{2} + x + 1}{x}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} + x + 1}{x} = \frac{x ^{2}}{x} + \frac{x}{x} + \frac{1}{x}

= \frac{x ^{2}}{x} + \frac{x}{x} + \frac{1}{x}

Apply rule

\frac{a}{a} = 1

\frac{x}{x} = 1

= \frac{x ^{2}}{x} + 1 + \frac{1}{x}

Cancel

\frac{x ^{2}}{x} : x

= x + 1 + \frac{1}{x}

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