Question

分式 计算题

第一题2x²/3y²×5y/6x÷10y/21x²
第二题a+b/ab+b-c/bc+c-a/ac
第三题1-x-y/x+2y÷x²-y²/x²+4xy+4y²
第四题(x-2/x+2-x+2/x-2))Xx²-4/x²

Answer 1

第一题2x²/3y²×5y/6x÷10y/21x²
=2x²/3y²×5y/6x×21x²/10y
=x/y×1/6×7x²/y
=7x^3 /(6y^2)

第二题(a+b)/(ab)+(b-c)/(bc)+(c-a)/(ac)
=1/b+1/a + 1/c-1/b + 1/a-1/c
=1/a + 1/a
=2/a

第三题1-(x-y)/(x+2y)÷(x²-y²)/(x²+4xy+4y²)
= 1-(x-y)/(x+2y) × (x²+4xy+4y²)/(x²-y²)
= 1-(x-y)/(x+2y) × (x+2y)²/{(x+y)(x-y)}
= 1- (x+2y)/(x+y)
= (x+y-x-2y)/(x+y)
= -y/(x+y)

第四题{ (x-2)/(x+2)-(x+2)/(x-2) } × (x²-4)/x²
= { (x-2)/(x+2) -(x+2)/(x-2) } × (x+2)(x-2) /x²
= { (x-2)/(x+2) × (x+2)(x-2) -(x+2)/(x-2)× (x+2)(x-2) } /x²
= { (x-2)^2 -(x+2)^2 } /x²
= -4x /x²
= -4/x