Đáp án:
`x=6`
Giải thích các bước giải:
`(2x-7)/(x²+5x-6)+3/(x²+9x+18)=1/(x+3)(ĐKXĐ:``x`$\neq$`1,x` $\neq$ `-6,x`$\neq$ `-3)`
`⇔(2x-7)/(x²+6x-x-6)+3/(x²+3x+6x+18)=1/(x+3)`
`⇔(2x-7)/[x(x+6)-(x+6)]+3/[x(x+3)+6(x+3)]=1/(x+3)`
`⇔(2x-7)/[(x+6)(x-1)]+3/[(x+3)(x+6)]=1/(x+3)`
`⇔[(2x-7)(x+3)]/[(x-1)(x+3)(x+6)]+[3(x-1)]/[(x-1)(x+3)(x+6)]=[(x-1)(x+6)]/[(x-1)(x+3)(x+6)]`
`⇒(2x-7)(x+3)+3(x-1)=(x-1)(x+6)`
`⇔2x²+6x-7x-21+3x-3=x²+6x-x-6`
`⇔2x²+2x-24=x²+5x-6`
`⇔2x²+2x-24-x²-5x+6=0`
`⇔x²-3x-18=0`
`⇔x²-6x+3x-18=0`
`⇔x(x-6)+3(x-6)=0`
`⇔(x-6)(x+3)=0`
`⇔`\(\left[ \begin{array}{l}x-6=0\\x+3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=6(TM ĐKXĐ)\\x=-3(Ko TM ĐKXĐ)\end{array} \right.\)
Vậy `x=6`
