\(a,\dfrac{3x+1}{4}=\dfrac{x+2}{3}\\ \Leftrightarrow9x+3=4x+8\\ \Leftrightarrow5x=5\\ \Leftrightarrow x=1\\ b,ĐKXĐ:x\ne0,x\ne5\\ \dfrac{x-3}{x-5}+\dfrac{1}{x}=\dfrac{x+5}{x\left(x-5\right)}\\ \Leftrightarrow\dfrac{x\left(x-3\right)}{x\left(x-5\right)}+\dfrac{x-5}{x\left(x-5\right)}-\dfrac{x+5}{x\left(x-5\right)}=0\\ \Leftrightarrow\dfrac{x^2-3x+x-5-x-5}{x\left(x-5\right)}=0\\ \Rightarrow x^2-3x-10=0\\ \Leftrightarrow\left(x-5\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5\left(ktm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)
\(c,ĐKXĐ:x\ne0,x\ne-1\\ \dfrac{x+3}{x+1}+\dfrac{x-3}{x}=2\\ \Leftrightarrow\dfrac{x\left(x+3\right)}{x\left(x+1\right)}+\dfrac{\left(x-3\right)\left(x+1\right)}{x\left(x+1\right)}-\dfrac{2x\left(x+1\right)}{x\left(x+1\right)}=0\\ \Leftrightarrow\dfrac{x^2+3x+x^2-2x-3-2x^2-2x}{x\left(x+1\right)}=0\\ \Rightarrow-x-3=0\\ \Leftrightarrow x=-3\left(tm\right)\)
\(d,ĐKXĐ:x\ne0,x\ne-2\\ \dfrac{7}{x}-\dfrac{5}{x+2}=0\\ \Leftrightarrow\dfrac{7\left(x+2\right)}{x\left(x+2\right)}-\dfrac{5x}{x\left(x+2\right)}=0\\ \Leftrightarrow\dfrac{7x+14-5x}{x\left(x+2\right)}=0\\ \Rightarrow2x+14=0\\ \Leftrightarrow x=-7\left(tm\right)\)
