Đáp án + Giải thích các bước giải:
`b)` `(4x+7)/(2x+2)-(3x+6)/(2x+2)(x ne -1)`
`=(4x+7-3x-6)/(2x+2)`
`=(x+1)/(2x+2)`
`=(x+1)/[2(x+1)]=1/2`
`c)` `(x^3+2x)/(x^3+1)+(2x)/(x^2-x+1)+1/(x+1)(xne-1)`
`=(x^3+2x)/[(x+1)(x^2-x+1)]+[2x(x+1)]/[(x+1)(x^2-x+1)]+(x^2-x+1)/[(x+1)(x^2-x+1)]`
`=(x^3+2x+2x^2+2x+x^2-x+1)/[(x+1)(x^2-x+1)]`
`=(x^3+3x^2+3x+1)/[(x+1)(x^2-x+1)]`
`=(x+1)^3/[(x+1)(x^2-x+1)]`
`=(x+1)^2/(x^2-x+1)`
`d)` `7/x-x/(x+6)+36/(x^2+6x)(xne0,xne-6)`
`=[7(x+6)]/[x(x+6)]-(x^2)/[x(x+6)]+36/[x(x+6)]`
`=(7x+42-x^2+36)/[x(x+6)]`
`=[7(x+6)-(x^2-36)]/[x(x+6)]`
`=[7(x+6)-(x-6)(x+6)]/[x(x+6)]`
`=[(x+6)(7-x+6)]/[x(x+6)]`
`=[(x+6)(13-x)]/[x(x+6)]=(13-x)/x`
`e)` `1/(x^2-x+1)+1-x^2/(x^3+1)(xne-1)`
`=(x+1)/[(x+1)(x^2-x+1)]+[(x+1)(x^2-x+1)]/[(x+1)(x^2-x+1)]-x^2/[(x+1)(x^2-x+1)]`
`=(x+1+x^3+1-x^2)/[(x-1)(x^2+x+1)]`
`=(x^3-x^2+x+2)/[(x-1)(x^2+x+1)]`.