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

פתרון

expand

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

\frac{1}{x ^{4} - 4 x ^{3} + 5 x ^{2} - 2 x}

צעדי פתרון

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

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

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

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

הרחב את:

x^{4} - 4 x^{3} + 5 x^{2} - 2 x

= \frac{1}{x ^{4} - 4 x ^{3} + 5 x ^{2} - 2 x}

(a cos (x) + b sin (x)) (a sin (x) + b cos (x))

cos (x) (4 cos^{2} (x) - 3)

40 (\frac{3}{8} x - \frac{2}{5} = \frac{7}{4})

6 x - 3 - 3 (x + 2)

\frac{y ^{3} - 6 y + 8}{y}