分式加减(1)(a+2⼀a눀-2a + 8⼀4-a눀)÷a-2⼀a。在线等啊急急急急急急急急

2025-04-29 03:13:04
推荐回答(1个)
回答1:

(1)(a+2/a²-2a + 8/4-a²)÷a-2/a
=[(a+2)/(a²-2a) + 8/(4-a²)÷(a-2)/a
=[(a+2)/a(a-2) -8/(a+2)(a-2)]Xa/(a-2)
={[(a+2)²-8a]/a(a+2)(a-2)}Xa/(a-2)
=[(a²+4a+4-8a]/(a+2)(a-2)²
=(a-2)²/(a+2)(a-2)²
=1/(a+2)
(2)x²+x/x-1 ÷ x²-1/x²-2x+1 - (2x-1)
=x(x+1)/(x-1)÷(x+1)(x-1)/(x-1)²-(2x-1)
=x(x+1)/(x-1)÷(x+1)/(x-1)-(2x-1)
=x(x+1)/(x-1)*(x-1)/(x+1)-(2x-1)
=x-(2x-1)
=1-x
(3)1/2x - 1/x+y · (x+y/2x - x-y)
=1/2x-1/(x+y)·(x+y)/2x-(x+y)
=1/2x-1/2x-(x+y)
=-x-y
(4)x-y/x+3y ÷ x²-y²/x²+6xy+9y² - 2y/x+y
=(x-y)/(x+3y) ÷ (x²-y²)/(x²+6xy+9y²) - 2y/(x+y)
=(x-y)/(x+3y) ·(x+3y)²/[ (x+y)(x-y)]- 2y/(x+y)
=(x+3y)/(x+y)- 2y/(x+y)
=(x+3y-2y)/(x+y)
=(x+y)/(x+y)
=1
(5)2/a²-4 · (a²+4/4a -1)÷ (1/2-1/a)其中a=1/2
=2/(a²-4 )·(a²+4/4a -1)÷(1/2-1/a)
=2/(a+2)(a-2)·[(a²+4)/4a -1]÷(a-2)/2a
=2/(a+2)(a-2)·(a²-4a+4)/4a÷(a-2)/2a
=2/(a+2)(a-2)·(a-2)²/4a·2a/(a-2)
=1/(a+2) 其中a=1/2
=1/(1/2+2)
=2/5