Question

\(\dfrac{1}{x}+\dfrac{1}{x+2}=\dfrac{5}{12}\)

giải pt ạ

Answer 1

`1/x+1/(x+2)=5/12`

ĐK:`x ne 0,x ne -2`

`<=>(x+2+x)/(x^2+2x)=5/12`

`<=>(2x+2)/(x^2+2x)=5/12`

`<=>24x+24=5x^2+10x`

`<=>5x^2-14x-24=0`

Ta có:`Delta'=49+24.5`

`=49+120=169`

`=>x_1=-6/5,x_2=4`

Vậy `S={4,-6/5}`

Answer 2

$ĐKXĐ : x \neq 0, x \neq -2$

Ta có : $\dfrac{1}{x} + \dfrac{1}{x+2} = \dfrac{5}{12}$

$\to \dfrac{2x+2}{x.(x+2)} = \dfrac{5}{12}$

$\to (2x+2).12 = x.(x+2).5$

$\to 24x + 24 = 5x^2 + 10x$

$\to 5x^2 - 14x - 24 = 0 $

$\to (x-4).(5x+6) = 0 $

S\to$ \(\left[{}\begin{matrix}x=4\\x=-\dfrac{6}{5}\end{matrix}\right.\)  ( thỏa mãn ĐKXĐ )

Vậy :....