Đáp án:
`a)(2y)/[3(x+y)²]`
`b)(x-y)/(x+y)`
`c)[3(x-2)]/[x(x²+2x+4)]`
`d)[7(x+1)]/(3x)`
`e)(2a)/(c+d)`
`f)-x/(x+y)`
Giải thích các bước giải:
`a)(10xy²(x+y))/(15xy(x+y)³)`
`=[5xy(x+y).2y]/[5xy(x+y).3(x+y)²]`
`=(2y)/[3(x+y)²]`
`b)(x²-xy-x+y)/(x²+xy-x-y)`
`=[x(x-y)-(x-y)]/[x(x+y)-(x+y)]`
`=[(x-y)(x-1)]/[(x+y)(x-1)]`
`=(x-y)/(x+y)`
`c)(3x²-12x+12)/(x^4-8x)`
`=[3(x²-4x+4)]/[x(x^3-8)]`
`=[3(x-2)²]/[x(x-2)(x²+2x+4)]`
`=[3(x-2)]/[x(x²+2x+4)]`
`d)(7x²+14x+7)/(3x²+3x)`
`=[7(x²+2x+1)]/[3x(x+1)]`
`=[7(x+1)²]/[3x(x+1)]`
`=[7(x+1)]/(3x)`
`e)(2a²-2ab)/(ac+ad-bc-bd)`
`=[2a(a-b)]/[a(c+d)-b(c+d)]`
`=[2a(a-b)]/[(c+d)(a-b)]`
`=(2a)/(c+d)`
`f)(x²-xy)/(y²-x²)`
`=[x(x-y)]/[-(x²-y²)]`
`=[x(x-y)]/[-(x+y)(x-y)]`
`=-x/(x+y)`
