Đáp án + Giải thích các bước giải:
Bài `1` :
`1.` `y/(3x)+(2y)/(3x)=(y+2y)/(3x)=(3y)/(3x)=y/x (x ne 0)`
`2.` `[6x^3(2y+1)]/(5y)*15/[2x^3(2y+1)] (x,y ne 0)`
`=[6x^3(2y+1)*15]/[5y*2x^3(2y+1)]`
`=(6*15)/(5y*2)=90/(10y)=9/y`
`3.` `3/(x^2-1):(6x)/(x^2+2x+1)(x ne pm 1,x ne 0)`
`=3/[(x-1)(x+1)]*(x^2+2x+1)/(6x)`
`=(x^2+2x+1)/[(x-1)(x+1)*2x]`
`=[(x+1)^2]/[(x-1)(x+1)*2x]`
`=(x+1)/[2x(x-1)]`
`4.` `(1-3x)/(2x)+(3x-2)/(2x-1)-(3x-2)/(4x^2-2x)(xne0,xne1/2)`
`=[(1-3x)(2x-1)]/[2x(2x-1)]+[(3x-2)*2x]/[2x(2x-1)]-(3x-2)/[2x(2x-1)]`
`=(2x-1-6x^2+3x+6x^2-4x-3x+2)/[2x(2x-1)]`
`=(1-2x)/[2x(2x-1)]`
`=[-(2x-1)]/[2x(2x-1)]=(-1)/(2x)`.
