Question

`(x+1)/5=(x+2)/4=(x+3)/3+(x+2)/4`

Answer 1

`(x+1)/5+(x+2)/4=(x+3)/3+(x+2)/4`

`=>(x+1)/5+1+(x+2)/4+1=(x+3)/3+1+(x+2)/4+1`

`=>(x+6)/5+(x+6)/4=(x+6)/3+(x+6)/4`

`=>(x+6)(1/5+1/4-1/3-1/4)=0`

`=>x+6=0`

`=>x=-6`

Vậy `S={-6}`

Answer 2

Sửa đề: \(\dfrac{x+1}{5}+\dfrac{x+2}{4}=\dfrac{x+3}{3}+\dfrac{x+2}{4}\)

Ta có: \(\dfrac{x+1}{5}+\dfrac{x+2}{4}=\dfrac{x+3}{3}+\dfrac{x+2}{4}\)

\(\Leftrightarrow\dfrac{x+1}{5}=\dfrac{x+3}{3}\)

\(\Leftrightarrow5\left(x+3\right)=3\left(x+1\right)\)

\(\Leftrightarrow5x+15=3x+3\)

\(\Leftrightarrow5x-3x=3-15\)

\(\Leftrightarrow2x=-12\)

hay x=-6

Vậy: x=-6

Answer 3

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Answer 4

\(\Leftrightarrow\dfrac{x+1}{5}+1=\dfrac{x+3}{3}+1\)

\(\Leftrightarrow\dfrac{x+6}{5}-\dfrac{x+6}{3}=0\)

\(\Leftrightarrow x+6=0\Leftrightarrow x=-6\)