Question

2x-5/x-4 = 2x+1/x+2

Answer 1

ĐK: `x \ne 4 ;x \ne -2`

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

`<=> (2x-5)(x+2)=(x-4)(2x+1)`

`<=> 2x^2 +4x-5x-10=2x^2+x-8x-4`

`<=>-x-10=-7x-4`

`<=>7x-x=-4+10`

`<=>6x=6`

`<=>x=1` (TM)

Vậy `x=1`.

Answer 2

\(\dfrac{2x-5}{x-4}=\dfrac{2x+1}{x+2}\)

\(< =>\left(2x-5\right)\left(x+2\right)=\left(x-4\right)\left(2x+1\right)\)

\(< =>2x^2-5x+4x-10=2x^2-8x+x-4\)

\(< =>2x^2-x-10-2x^2+7x+4=0\)

\(< =>6x-6=0\)

\(< =>6x=6\)

\(< =>x=6:6=1\)

Vậy....

Answer 3

\(\dfrac{2x-5}{x-4}=\dfrac{2x+1}{x+2}\) (1)

ĐKXĐ: x ≠ 4; x ≠ -2

PT (1) \(\Leftrightarrow\left(2x-5\right)\left(x+2\right)=\left(x-4\right)\left(2x+1\right)\)

\(\Leftrightarrow2x^2+4x-5x-10=2x^2+x-8x-4\)

\(\Leftrightarrow2x^2+4x-5x-10-2x^2-x+8x+4=0\)

\(\Leftrightarrow6x-6=0\)

<=> 6x = 6

<=> x = 1

Vậy S = {1}