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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

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

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

\frac{2500 s ( 20 s + 200 )}{( s + 1 ) ( s ^{2} + 100 s + 10000 )}

\frac{( x - 2 ) ( x - 4 )}{4}

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

- \frac{2 s ( - s ^{2} - 27 )}{( s ^{2} - 9 ) ^{3}}

2 (\frac{x ^{2}}{2} + t^{2} + t = c)

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