Question

GIẢI PHƯƠNG TRÌNH 

`(x+3)/(x-3) + (x-2)/x = 2`

 

` (x^2-6)/x = x + 3/2`

Answer 1

a: ĐKXĐ: \(x\notin\left\{3;0\right\}\)

\(\dfrac{x+3}{x-3}+\dfrac{x-2}{x}=2\)

=>\(\dfrac{x\left(x+3\right)+\left(x-2\right)\left(x-3\right)}{x\left(x-3\right)}=2\)

=>\(2x\left(x-3\right)=x\left(x+3\right)+\left(x-2\right)\left(x-3\right)\)

=>\(2x^2-6x=x^2+3x+x^2-5x+6=2x^2-2x+6\)

=>-6x=-2x+6

=>-4x=6

=>\(x=-\dfrac{3}{2}\left(nhận\right)\)

b: ĐKXĐ: x<>0

\(\dfrac{x^2-6}{x}=x+\dfrac{3}{2}\)

=>\(\dfrac{x^2-6}{x}=\dfrac{2x+3}{2}\)

=>\(2\left(x^2-6\right)=x\left(2x+3\right)\)

=>\(2x^2+3x=2x^2-12\)

=>3x=-12

=>x=-4(nhận)