What is expand ((n^2+n)^2)/(n^4) ?

The solution to expand ((n^2+n)^2)/(n^4) is 1+2/n+1/(n^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ((n^2+n)^2)/(n^4)

expand

\frac{( n ^{2} + n ) ^{2}}{n ^{4}}

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

Solution steps

\frac{( n ^{2} + n ) ^{2}}{n ^{4}}

(n^{2} + n)^{2} = n^{4} + 2 n^{3} + n^{2}

= \frac{n ^{4} + 2 n ^{3} + n ^{2}}{n ^{4}}

Factor

n^{4} + 2 n^{3} + n^{2} : n^{2} (n^{2} + 2 n + 1)

= \frac{n ^{2} ( n ^{2} + 2 n + 1 )}{n ^{4}}

Cancel

\frac{n ^{2} ( n ^{2} + 2 n + 1 )}{n ^{4}} : \frac{n ^{2} + 2 n + 1}{n ^{2}}

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

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

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

Cancel

\frac{2 n}{n ^{2}} : \frac{2}{n}

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

\frac{d}{d t} ((s) (ln (t) + 4 t))

\frac{x ^{2} c}{( x + a ) ( x + b )}

(3 - x y cos (x y)) d x - x^{2} cos (x y) d y

\frac{x x + h + 3 - h x + 3}{( x - 4 ) ( x + h - 4 )}

\frac{( a ^{2} - 4 ) ^{4} a ^{2} - 4}{a}

What is expand ((n^2+n)^2)/(n^4) ?
The solution to expand ((n^2+n)^2)/(n^4) is 1+2/n+1/(n^2)