2/(x+1)-3/(x-2)=5/2. Tìm x?????!!!!!

Đáp án:

Phương trình vô nghiệm

Giải thích các bước giải:

$\dfrac{2}{x+1}-\dfrac{3}{x-2}=\dfrac{5}{2}\,\,\,(x\ne-1;x\ne2)\\⇔\dfrac{2}{x+1}-\dfrac{3}{x-2}-\dfrac{5}{2}=0\\⇔\dfrac{2.2(x-2)-3.2(x+1)-5(x+1)(x-2)}{2(x+1)(x-2)}=0\\⇔\dfrac{4x-8-6x-6-5(x^2-x-2)}{2(x+1)(x-2)}=0\\⇔\dfrac{-2x-14-5x^2+5x+10}{2(x+1)(x-2)}=0\\⇔\dfrac{-5x^2+3x-4}{2(x+1)(x-2)}=0\\\to 5x^2-3x+4=0$

Ta có:

$5x^2-3x+4\\=5\left(x^2-\dfrac{3}{5}x+\dfrac{4}{5}\right)\\=5\left(x^2-2.x.\dfrac{3}{10}+\left(\dfrac{3}{10}\right)^2+\dfrac{71}{100}\right)\\=5\left(x-\dfrac{3}{10}\right)^2+\dfrac{71}{20}>0\,\,\,\forall x$

Vậy phương trình vô nghiệm

Đáp án ` 8/5 `

Giải thích các bước giải:

$\dfrac{2}{x + 1}$`-`$\dfrac{3}{x - 2}$`= 5/2 `

`<=>`$\dfrac{2( x - 2 )}{( x + 1 ) ( x - 2 ) }$`-`$\dfrac{3( x + 1 )}{( x + 1 ) ( x - 2 ) }$`= 5/2`

`<=>`$\dfrac{2x - 4}{( x + 1 ) ( x - 2 )}$`-`$\dfrac{3x + 3}{( x + 1 ) ( x - 2 )}$`= 5/2 `

`<=>`$\dfrac{2x - 4 - 3x - 3}{( x - 1 ) ( x - 2 ) }$`= 5/2 `

`<=>`$\dfrac{- ( x + 1 ) }{( x + 1 ) ( x - 2 )}$`= 5/2 `

`<=>`$\dfrac{- 1}{x - 2}$`= 5/2`

`<=>`$\dfrac{ - 1 . 2}{2( x - 2 )}$`=`$\dfrac{5( x - 2 )}{2( x - 2 ) }$

`=> - 2 = 5( x - 2 ) `

`<=> - 2 = 5x - 10 `

`<=> - 5x = - 10 + 2 `

`<=> - 5x = - 8 `

`<=> x = 8/5 `

Vậy `x =  8/5 `