a) \(x^3-3x^2+5x-15\ne0\)
\(\Rightarrow x^2\left(x-3\right)+5\left(x-3\right)\ne0\)
\(\Rightarrow\left(x-3\right)\left(x^2+5\right)\)
=> ĐKXĐ: x khác 3
b) \(D=\dfrac{1}{5}\)
\(\Rightarrow\dfrac{2x-6}{\left(x-3\right)\left(x^2+5\right)}=\dfrac{1}{5}\)
\(\Rightarrow\dfrac{2\left(x-3\right)}{\left(x-3\right)\left(x^2+5\right)}=\dfrac{1}{5}\)
\(\Rightarrow\dfrac{2}{x^2+5}=\dfrac{1}{5}\)
\(\Rightarrow x^2+5=2:\dfrac{1}{5}\)
\(\Rightarrow x^2+5=10\)
\(\Rightarrow x^2=10-5=5\)
\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{5}\\x=-\sqrt{5}\end{matrix}\right.\)
c) \(D=\dfrac{1}{x^2+1}\)
\(\Rightarrow\dfrac{2x-6}{\left(x-3\right)\left(x^2+5\right)}=\dfrac{1}{x^2+1}\)
\(\Rightarrow\dfrac{2\left(x-3\right)}{\left(x-3\right)\left(x^2+5\right)}=\dfrac{1}{x^2+1}\)
\(\Rightarrow\dfrac{2}{x^2+5}=\dfrac{1}{x^2+1}\)
\(\Rightarrow x^2+5=2\left(x^2+1\right)\)
\(\Rightarrow x^2+5=2x^2+2\)
\(\Rightarrow x^2+5-2x^2-2=0\)
\(\Rightarrow-x^2+3=0\)
\(\Rightarrow x^2=3\)
\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{3}\\x=-\sqrt{3}\end{matrix}\right.\)
