Đáp án + Giải thích các bước giải:
`1//7+x=19-3x`
`⇔x+3x=19-7`
`<=>4x=12`
`<=>x=3`
Vậy `S={3}`
`2//2(x-2)=3x+8`
`<=>2x-4=3x+8`
`<=>2x-3x=4+8`
`<=>-x=12`
`<=>x=-12`
Vậy `S={-12}`
`3//2x(x+1)+7x=0`
`<=>2x^{2}+2x+7x=0`
`<=>2x^{2}+9x=0`
`<=>x(2x+9)=0`
`⇔` \(\left[ \begin{array}{l}x=0\\2x+9=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=0\\x=-\frac{9}{2}\end{array} \right.\)
Vậy `S={0;-(9)/(2)}`
`4//(x+1)/(x+3)+(x)/(x-2)=2` `(ĐKXĐ:x\ne{-3;2})`
`⇔((x+1)(x-2))/((x+3)(x-2))+(x(x+3))/((x-2)(x+3))=(2(x-2)(x+3))/((x-2)(x+3))`
`⇒(x+1)(x-2)+x(x+3)=2(x-2)(x+3)`
`⇔x^{2}-x-2+x^{2}+3x=2x^{2}+2x-12`
`⇔(x^{2}+x^{2}-2x^{2})+(-x+3x-2x)+(-2+12)=0`
`⇔0x+10=0`
`<=>0x=-10` ( Vô nghiệm )
Vậy phương trình vô nghiệm `(S=∅)`
`5//(x+3)(2x-1)=0`
`⇔` \(\left[ \begin{array}{l}x+3=0\\2x-1=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-3\\x=\frac{1}{2}\end{array} \right.\)
Vậy `S={-3;(1)/(2)}`
`6//2x(x+1)=(x+1)(x-2)`
`<=>2x(x+1)-(x+1)(x-2)=0`
`<=>(x+1)(2x-x+2)=0`
`<=>(x+1)(x+2)=0`
`⇔` \(\left[ \begin{array}{l}x+1=0\\x+2=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-1\\x=-2\end{array} \right.\)
Vậy `S={-1;-2}`
`7//(3-x)/(5)+(7-x)/(10)=(1)/(2)`
`<=>(2(3-x))/(10)+(7-x)/(10)=(5)/(10)`
`⇒6-2x+7-x=5`
`⇔-2x-x=-6-7+5`
`<=>-3x=-8`
`<=>x=(8)/(3)`
Vậy `S={(8)/(3)}`
`8//(x+2)/(x-2)+(x-2)/(x+2)=(2x^{2})/(x^{2}-4)` `(ĐKXĐ:x\ne±2)`
`⇔((x+2)^{2})/((x-2)(x+2))+((x-2)^{2})/((x+2)(x-2))=(2x^{2})/((x-2)(x+2))`
`⇔(x+2)^{2}+(x-2)^{2}=2x^{2}`
`<=>x^{2}+4x+4+x^{2}-4x+4=2x^{2}`
`<=>2x^{2}+8=2x^{2}`
`<=>2x^{2}-2x^{2}=-8`
`<=>0x^{2}=-8` ( Vô nghiệm )
Vậy phương trình vô nghiệm `(S=∅)`
