化简 (sqrt((1+x^2)(1+y^2))-1)/(x^2+y^2)-1/2

解答

化简

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

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

求解步骤

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

x^{2} + y^{2}, 2

的最小公倍数:

2 (x^{2} + y^{2})

根据最小公倍数调整分式

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

使用分式法则:

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

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

化简

((1 + x^{2}) (1 + y^{2}) - 1) \cdot 2 - (x^{2} + y^{2}) : 2 (1 + x^{2}) (1 + y^{2}) - 2 - x^{2} - y^{2}

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

e x p an d cos (7 x^{2} (x - 3))

s im pl i f y (6 - 2 x + 1)^{2}

e x p an d \frac{( x + 3 ) ( x - 7 )}{( x + 4 ) ( x - 5 )}

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

e x p an d \frac{8640 e ^{- 0.96 t}}{( 1 + 3 e ^{- 0.96 t} ) ^{2}}