Đáp án:
Giải thích các bước giải:
`a)3x+21=0`
`<=>3x=-21`
`<=>x=-7`
Vậy `S={-7}`
`b)(2x+1)(5-x)=0`
`<=>` \(\left[ \begin{array}{l}2x+1=0\\5-x=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=-\dfrac{1}{2}\\x=5\end{array} \right.\)
Vậy `S={-1/2;5}`
`c)` `x/5+1/2=1`
`<=>(2x)/10+5/10=10/10`
`<=>2x+5=10`
`<=>2x=5`
`<=>x=5/2`
Vậy `S={5/2}`
`d)` `(x-1)/x+x/5=1` (đk: `x\ne0`)
`<=>(5(x-1)+x^2)/(5x)=(5x)/(5x)`
`=>x^2+5x-5=5x`
`<=>x^2+5x-5x-5=0`
`<=>x^2=5`
`<=>x=+-sqrt{5}`
Vậy `S={+-sqrt{5}}`
`e)` `(x-1)/(x-2)+(x+3)/(x-4)=2/((x-2)(4-x))` (đk: `x\ne2;x\ne4`)
`<=>(x-1)/(x-2)+(x+3)/(x-4)=(-2)/((x-2)(x-4))`
`<=>((x-1)(x-4)+(x+3)(x-2))/((x-2)(x-4))=(-2)/((x-2)(x-4))`
`=>x^2-5x+4+x^2+x-6=-2`
`<=>2x^2-4x=0`
`<=>2x(x-2)=0`
`<=>` \(\left[ \begin{array}{l}2x=0\\x-2=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=0(tmđk)\\x=2(ktmđk)\end{array} \right.\)
Vậy `S={0}`
