第一題2x²/3y²×5y/6x÷10y/21x²
=2x²/3y²×5y/6x×21x²/10y
=x/y×1/6×7x²/y
=7x^3 /(6y^2)
第二題(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
第三題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)
第四題{ (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