a/ \(\dfrac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}=0\)
\(\Leftrightarrow\dfrac{x^3\left(x+1\right)+\left(x+1\right)}{x^4-x^3+x^2+x^2-x+1}=0\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x^3+1\right)}{x^2\left(x^2-x+1\right)+\left(x^2-x+1\right)}=0\)
\(\Leftrightarrow\dfrac{\left(x+1\right)^2\left(x^2-x+1\right)}{\left(x^2+1\right)\left(x^2-x+1\right)}=0\)
\(\Leftrightarrow\dfrac{\left(x+1\right)^2}{x^2+1}=0\)
\(\Leftrightarrow\left(x+1\right)^2=0\)
\(\Leftrightarrow x=-1\)
Vậy ...
b/ \(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}=0\)
\(\Leftrightarrow\dfrac{x^4-x^2-4x^2+4}{x^4-x^2-9x^2+9}=0\)
\(\Leftrightarrow\dfrac{x^2\left(x^2-1\right)-4\left(x^2-1\right)}{x^2\left(x^2-1\right)-9\left(x^2-1\right)}=0\)
\(\Leftrightarrow\dfrac{\left(x^2-1\right)\left(x^2-4\right)}{\left(x^2-1\right)\left(x^2-9\right)}=0\)
\(\Leftrightarrow\dfrac{\left(x-2\right)\left(x+2\right)}{x^2-9}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy..
