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受欢迎的代数 >

化简 ((t-3))/((5-t))-((t+4))/((t+5))+((t-2))/((25-t^2))

解答

化简

\frac{( t - 3 )}{( 5 - t )} - \frac{( t + 4 )}{( t + 5 )} + \frac{( t - 2 )}{( 25 - t ^{2} )}

解答

- \frac{2 t ^{2} + 2 t - 37}{( t - 5 ) ( t + 5 )}

求解步骤

\frac{t - 3}{5 - t} - \frac{t + 4}{t + 5} + \frac{t - 2}{25 - t ^{2}}

5 - t, t + 5, 25 - t^{2}

的最小公倍数:

(- t + 5) (t + 5) (t - 5)

根据最小公倍数调整分式

= \frac{- ( t - 3 ) ( - t + 5 ) ( t + 5 )}{( - t + 5 ) ( t + 5 ) ( t - 5 )} - \frac{( t + 4 ) ( - t + 5 ) ( t - 5 )}{( - t + 5 ) ( t + 5 ) ( t - 5 )} + \frac{( t - 2 ) ( t - 5 )}{( - t + 5 ) ( t + 5 ) ( t - 5 )}

使用分式法则:

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

= \frac{- ( t - 3 ) ( - t + 5 ) ( t + 5 ) - ( t + 4 ) ( - t + 5 ) ( t - 5 ) + ( t - 2 ) ( t - 5 )}{( - t + 5 ) ( t + 5 ) ( t - 5 )}

化简

- (t - 3) (- t + 5) (t + 5) - (t + 4) (- t + 5) (t - 5) + (t - 2) (t - 5) : - (t - 3) (- t + 5) (t + 5) + (t + 4) (t - 5)^{2} + (t - 2) (t - 5)

= \frac{- ( t - 3 ) ( - t + 5 ) ( t + 5 ) + ( t + 4 ) ( t - 5 ) ^{2} + ( t - 2 ) ( t - 5 )}{( - t + 5 ) ( t + 5 ) ( t - 5 )}

化简

- (t - 3) (- t + 5) (t + 5) + (t + 4) (t - 5)^{2} + (t - 2) (t - 5) : 2 t^{3} - 8 t^{2} - 47 t + 185

= \frac{2 t ^{3} - 8 t ^{2} - 47 t + 185}{( - t + 5 ) ( t + 5 ) ( t - 5 )}

消掉

\frac{2 t ^{3} - 8 t ^{2} - 47 t + 185}{( - t + 5 ) ( t + 5 ) ( t - 5 )} : - \frac{2 t ^{2} + 2 t - 37}{( t - 5 ) ( t + 5 )}

= - \frac{2 t ^{2} + 2 t - 37}{( t - 5 ) ( t + 5 )}

流行的例子

s im pl i f y 3 x + 2 y

化简 sqrt(12)x^4

s im pl i f y 12 x^{4}

solvefor x,x>= 6

so l v e f or x, x \geq 6

quadraticformula (x-6)(x+2)=0

q u a d r a t i c f or m u l a (x - 6) (x + 2) = 0

s im pl i f y \frac{36}{240}