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

The solution to expand ((x+2)(x+5))/(x^2) is 1+7/x+(10)/(x^2)

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

expand

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

1 + \frac{7}{x} + \frac{10}{x ^{2}}

Solution steps

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

Expand

(x + 2) (x + 5) : x^{2} + 7 x + 10

= \frac{x ^{2} + 7 x + 10}{x ^{2}}

Apply the fraction rule:

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

\frac{x ^{2} + 7 x + 10}{x ^{2}} = \frac{x ^{2}}{x ^{2}} + \frac{7 x}{x ^{2}} + \frac{10}{x ^{2}}

= \frac{x ^{2}}{x ^{2}} + \frac{7 x}{x ^{2}} + \frac{10}{x ^{2}}

Apply rule

\frac{a}{a} = 1

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

= 1 + \frac{7 x}{x ^{2}} + \frac{10}{x ^{2}}

Cancel

\frac{7 x}{x ^{2}} : \frac{7}{x}

= 1 + \frac{7}{x} + \frac{10}{x ^{2}}

\frac{3 ( 4 s + 19 )}{( 2 s + 7 ) ( s + 4 )}

x + Δ x (x + Δ x - 4)

11 x^{5 \cdot (2 m + 1)}

\frac{( x ^{2} + 1 ) ^{2}}{x ^{4}}

(\cdot + y) (3 + z)

What is expand ((x+2)(x+5))/(x^2) ?
The solution to expand ((x+2)(x+5))/(x^2) is 1+7/x+(10)/(x^2)