Đáp án+Giải thích các bước giải:
`a)(x+1)/(x+2):((x+2)/(x+3):(x+3)/(x+1))
`=(x+1)/(x+2):((x+2)/(x+3)*(x+1)/(x+3))`
`=(x+1)/(x+2):((x+2)(x+1))/(x+3)^2`
`=(x+1)/(x+2)*(x+3)^2/((x+2)(x+1)`
`=(x+3)^2/(x+2)^2`
`b)((3x)/(1-3x)+(2x)/(3x+1)):(6x^2+10x)/(1-6x+9x^2)`
`=((2x(3x-1))/((3x-1)(3x+1))-(3x(3x+1))/((3x-1)(3x+1))):(2x(3x+5))/(3x-1)^2`
`=(6x^2-2x-9x^2-3x)/((3x-1)(3x+1))*(3x-1)^2/(2x(3x+5))`
`=(-3x^2-5x)/((3x-1)(3x+1))*(3x-1)^2/(2x(3x+5))`
`=(-x(3x+5))/((3x-1)(3x+1))*(3x-1)^2/(2x(3x+5))`
`=(-(3x-1))/(2(3x+1))`
`c)(1/(x^2+x)-(2-x)/(x+1)):(1/x+x-2)`
`=(1/(x(x+1))+(x(x-2))/(x(x+1))):((x^2-2x+1)/x)`
`=((1+x^2-2x)/(x(x+1))*x/(x^2-2x+1)`
`=1/(x+1)`
`d)(9/(x^3-9x)+1/(x+3)):((x-3)/(x^2+3x)-x/(3x+9))`
`=(9/(x(x-3)(x+3))+(x(x-3))/(x(x-3)(x+3))):((3x-9)/(3x(x+3))-x^2/(3x(x+3)))`
`=((9+x^2-3x)/(x(x-3)(x+3))):((-(x^2-3x+9))/(3x(x+3)))`
`=(x^2-3x+9)/(x(x-3)(x+3)))*(3x(x+3))/(-(x^2-3x+9))`
`=-3/(x-3)`
