What is expand ((x+2)(x+3))/(x^2) ?

The solution to expand ((x+2)(x+3))/(x^2) is 1+5/x+6/(x^2)

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expand ((x+2)(x+3))/(x^2)

expand

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

1 + \frac{5}{x} + \frac{6}{x ^{2}}

Solution steps

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

Expand

(x + 2) (x + 3) : x^{2} + 5 x + 6

= \frac{x ^{2} + 5 x + 6}{x ^{2}}

Apply the fraction rule:

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

\frac{x ^{2} + 5 x + 6}{x ^{2}} = \frac{x ^{2}}{x ^{2}} + \frac{5 x}{x ^{2}} + \frac{6}{x ^{2}}

= \frac{x ^{2}}{x ^{2}} + \frac{5 x}{x ^{2}} + \frac{6}{x ^{2}}

Apply rule

\frac{a}{a} = 1

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

= 1 + \frac{5 x}{x ^{2}} + \frac{6}{x ^{2}}

Cancel

\frac{5 x}{x ^{2}} : \frac{5}{x}

= 1 + \frac{5}{x} + \frac{6}{x ^{2}}

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

2 e^{j (\frac{π}{4} + π)}

(e^{x} + e^{- x})^{8}

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

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

What is expand ((x+2)(x+3))/(x^2) ?
The solution to expand ((x+2)(x+3))/(x^2) is 1+5/x+6/(x^2)