Question

Answer 1

\(\dfrac{7}{8x}+\dfrac{5-x}{4x^2-8x}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8x-16}\left(x\notin\left\{0;2\right\}\right)\\ \Leftrightarrow\dfrac{7\left(x-2\right)}{8x\left(x-2\right)}+\dfrac{2\left(5-x\right)}{8x\left(x-2\right)}=\dfrac{4\left(x-1\right)}{8x\left(x-2\right)}+\dfrac{x}{8x\left(x-2\right)}\\ \Leftrightarrow7\left(x-2\right)+2\left(5-x\right)=4\left(x-1\right)+x\\ \Leftrightarrow7x-14+10-2x=4x-4+x\\ \Leftrightarrow5x-4=5x-4\\ \Leftrightarrow0=0\)

=> Pt vô số nghiệm với x khác 0 và khác 2