What is expand ((2x+5)(3x+4))/(x^2) ?

The solution to expand ((2x+5)(3x+4))/(x^2) is 6+(23)/x+(20)/(x^2)

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expand ((2x+5)(3x+4))/(x^2)

expand

\frac{( 2 x + 5 ) ( 3 x + 4 )}{x ^{2}}

6 + \frac{23}{x} + \frac{20}{x ^{2}}

Solution steps

\frac{( 2 x + 5 ) ( 3 x + 4 )}{x ^{2}}

Expand

(2 x + 5) (3 x + 4) : 6 x^{2} + 23 x + 20

= \frac{6 x ^{2} + 23 x + 20}{x ^{2}}

Apply the fraction rule:

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

\frac{6 x ^{2} + 23 x + 20}{x ^{2}} = \frac{6 x ^{2}}{x ^{2}} + \frac{23 x}{x ^{2}} + \frac{20}{x ^{2}}

= \frac{6 x ^{2}}{x ^{2}} + \frac{23 x}{x ^{2}} + \frac{20}{x ^{2}}

Cancel

\frac{6 x ^{2}}{x ^{2}} : 6

= 6 + \frac{23 x}{x ^{2}} + \frac{20}{x ^{2}}

Cancel

\frac{23 x}{x ^{2}} : \frac{23}{x}

= 6 + \frac{23}{x} + \frac{20}{x ^{2}}

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\frac{n ! ( n + 2 )}{( n + 1 )}

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What is expand ((2x+5)(3x+4))/(x^2) ?
The solution to expand ((2x+5)(3x+4))/(x^2) is 6+(23)/x+(20)/(x^2)