\(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}+\dfrac{3x-1}{x-4}\\ ĐKXĐ:x\ne-4;x\ne4\)
\(\Leftrightarrow\dfrac{5x^2-80}{x^2-16}=\dfrac{2x^2-8x-x+4}{x^2-16}+\dfrac{3x^2+12x-x-4}{x^2-16}\\ \Rightarrow5x^2-80=2x^2-9x+4+3x^2+11x-4\\ \Leftrightarrow5x^2-2x^2-3x^2+9x-11x=80-4+4\\ \Leftrightarrow-2x=80\\ \Leftrightarrow x=-40\left(nhận\right)\)
Vậy S = { -40 }
\(ĐKXĐ:x\ne\pm4\)
\(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}+\dfrac{3x-1}{x-4}\)
\(\Leftrightarrow\dfrac{5\left(x+4\right)\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}+\dfrac{76}{\left(x+4\right)\left(x-4\right)}=\dfrac{\left(2x-1\right)\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}+\dfrac{\left(3x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x-4\right)}\)
\(\Rightarrow5x^2-80+76=2x^2-9x+4+3x^2+11x-4\)
\(\Leftrightarrow-4=2x\)
\(\Leftrightarrow x=-2\left(nhận\right)\)
Vậy \(S=\left\{-2\right\}\)
