Question

Giải pt: \(\dfrac{12}{x-1}-\dfrac{8}{x+1}=1\)

Answer 1

\(\dfrac{12}{x-1}-\dfrac{8}{x+1}=1\)(ĐKXĐ: \(x\notin\left\{1;-1\right\}\))

=>\(\dfrac{12\left(x+1\right)-8\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=1\)

=>\(\left(x-1\right)\left(x+1\right)=12x+12-8x+8=4x+20\)

=>\(x^2-1-4x-20=0\)

=>\(x^2-4x-21=0\)

=>(x-7)(x+3)=0

=>\(\left[{}\begin{matrix}x=7\left(nhận\right)\\x=-3\left(nhận\right)\end{matrix}\right.\)