`#AkaShi`
a) 2(x+1)-3(x-3)=x-2
⇔2x+2-3x+9-x+2=0
⇔-2x=-13`
`⇔x=13/2`
Vậy `x=13/2`
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`b) (5x-14)/(x²-4)+1/(x-2)+x/(x+2)=0`
ĐKXĐ: `x \ne ±2`
`⇔(5x-14)/(x²-4)+(x+2)/(x²-4)+(x(x-2))/(x²-4)=0`
`⇔5x-14+x+2+x²-2x=0`
`⇔x²+4x-12=0`
`⇔x²-2x+6x-12=0`
`⇔x(x-2)+6(x-2)=0`
`⇔(x-2)(x+6)=0`
`1) x-2=0⇔x=2 (KTM)`
`⇔x+6=0⇔x=-6`
Vậy `S={-6}`
.....................
`x(x+1)-2x >= (x-2)²`
`⇔x²+x-2x >= x²-4x+4`
`⇔x²-x²-x+4x >= 4`
`⇔3x >= 4`
`⇔x >= 4/3`
Vậy `BPT` có nhiệm `x >= 4/3`
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`(x-2)/3-(2x+2)/8 < 1+(1+5x)/12`
`⇔(8(x-2))/24-(3(2x+2))/24 < 24/24+(2(1+5x))/24`
`⇔8x-16-6x-6 < 24+2+10x`
`⇔8x-6x-10x < 16+6+2+24`
`⇔-8x < 48 `
`⇔8x > -48`
`⇔x > -6`
Vậy `BPT` có nghiệm `x > -6`
