展开 ((a+x)(b+n-x))/((a+b+n)^2(a+b+n+1))

解答

展开

\frac{( a + x ) ( b + n - x )}{( a + b + n ) ^{2} ( a + b + n + 1 )}

\frac{ab + an - a x + b x + n x - x ^{2}}{a ^{3} + 3 a ^{2} b + 3 a ^{2} n + a ^{2} + 3 a b ^{2} + 2 ab + 3 a n ^{2} + 6 abn + 2 an + b ^{3} + b ^{2} + n ^{3} + 3 b n ^{2} + n ^{2} + 3 b ^{2} n + 2 bn}

求解步骤

\frac{( a + x ) ( b + n - x )}{( a + b + n ) ^{2} ( a + b + n + 1 )}

(a + b + n)^{2} = 2 ab + 2 an + a^{2} + b^{2} + 2 bn + n^{2}

= \frac{( x + a ) ( - x + b + n )}{( a ^{2} + 2 ab + 2 an + b ^{2} + 2 bn + n ^{2} ) ( a + b + n + 1 )}

乘开

(2 ab + 2 an + a^{2} + b^{2} + 2 bn + n^{2}) (a + b + n + 1) : a^{3} + 3 a^{2} b + 3 a^{2} n + a^{2} + 3 a b^{2} + 2 ab + 3 a n^{2} + 6 abn + 2 an + b^{3} + b^{2} + n^{3} + 3 b n^{2} + n^{2} + 3 b^{2} n + 2 bn

= \frac{( x + a ) ( - x + b + n )}{a ^{3} + 3 a ^{2} b + 3 a ^{2} n + a ^{2} + 3 a b ^{2} + 2 ab + 3 a n ^{2} + 6 abn + 2 an + b ^{3} + b ^{2} + n ^{3} + 3 b n ^{2} + n ^{2} + 3 b ^{2} n + 2 bn}

乘开

(a + x) (b + n - x) : ab + an - a x + b x + n x - x^{2}

= \frac{ab + an - a x + b x + n x - x ^{2}}{a ^{3} + 3 a ^{2} b + 3 a ^{2} n + a ^{2} + 3 a b ^{2} + 2 ab + 3 a n ^{2} + 6 abn + 2 an + b ^{3} + b ^{2} + n ^{3} + 3 b n ^{2} + n ^{2} + 3 b ^{2} n + 2 bn}

e x p an d (e^{4 x} - e^{- 4 x})^{2}

e x p an d V (0, + 6) F (0, + 10)

e x p an d \frac{( x + i y - 1 ) ^{2}}{( x + i y + 1 ) ^{2}}

e x p an d (2 x - 2 + \frac{c}{e ^{x}})^{2}

e x p an d \frac{4 x ^{2} + 3 x + 6}{x ^{2} ( x ^{2} + 3 )}