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

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

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expand (Δx(-x+1))/((x+Δx+1)(x+1))

expand

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

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

Solution steps

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

Expand

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

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

Expand

Δ x (- x + 1) : - Δ x^{2} + Δ x

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

(x^{2} - 6 x - 8) cos (x - 2)

\frac{25}{( 3 + 2 x ) ^{2} ( 1 - x )}

- 6 (π^{2} - 4) + \frac{3 π ^{2}}{4}

(\frac{2}{3} x + 2 y = 0,) (\frac{3}{4} x - 5 y = 8)

\frac{2 x ^{2} + 2 x + 10}{( x + 1 ) ( x ^{2} + 9 )}

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