What is expand (x(x+1)+1)/(x^2) ?

The solution to expand (x(x+1)+1)/(x^2) is 1+1/x+1/(x^2)

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expand (x(x+1)+1)/(x^2)

expand

\frac{x ( x + 1 ) + 1}{x ^{2}}

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

Solution steps

\frac{x ( x + 1 ) + 1}{x ^{2}}

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

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

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

Cancel

\frac{x}{x ^{2}} : \frac{1}{x}

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

π (4 x^{2} - 4 x + 1)

\frac{1}{( 1 + 3.5 x ) ( 1 - 2.5 x )}

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

ln (x^{3} y)

(3 t + 1) H (t - π)

What is expand (x(x+1)+1)/(x^2) ?
The solution to expand (x(x+1)+1)/(x^2) is 1+1/x+1/(x^2)