化简 (4sqrt(ab))/((sqrt(a)+\sqrt{b))^2}

解答

化简

\frac{4 ab}{( a + b ) ^{2}}

\frac{4 ab}{a + 2 a b + b}

求解步骤

\frac{4 ab}{( a + b ) ^{2}}

使用完全平方公式:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(a + b)^{2} = (a)^{2} + 2 a b + (b)^{2}

= \frac{4 ab}{( a ) ^{2} + 2 a b + ( b ) ^{2}}

化简

(a)^{2} + 2 a b + (b)^{2} : a + 2 a b + b

= \frac{4 ab}{a + 2 a b + b}

e x p an d \frac{1}{( 2 n - 1 ) ( 2 n + 1 )}

e x p an d \frac{2 ( 4 2 - 2 )}{3}

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

e x p an d (e^{x} + 1)^{3}

e x p an d (6 x + y^{2}) d x + y (2 x - 3 y) d y