What is expand (x+1)/(x(x+1))-((x-1)x)/(x(x+1)) ?

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

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expand (x+1)/(x(x+1))-((x-1)x)/(x(x+1))

expand

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

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

Solution steps

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

Apply rule

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

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

Expand

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

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

Expand

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

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

\frac{x}{( ( 0.012 - x ) \cdot ( 0.04 - 4 x ) ^{4} )}

(a x + b y) (c + d y)

(a^{\frac{9}{2}} - b^{\frac{9}{2}})^{2}

(sin (x))^{2} + (6 + cos (x))^{2}

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

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