a: DKXĐ: \(x\notin\left\{0;-1\right\}\)
\(\dfrac{x+3}{x+1}-\dfrac{x-1}{x}=\dfrac{x^2+5x+1}{x\left(x+1\right)}\)
=>\(\dfrac{x\left(x+3\right)-\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}=\dfrac{x^2+5x+1}{x\left(x+1\right)}\)
=>\(x^2+5x+1=x\left(x+3\right)-\left(x-1\right)\left(x+1\right)\)
=>\(x^2+5x+1=x^2+3x-x^2+1=3x+1\)
=>\(x^2+2x=0\)
=>x(x+2)=0
=>\(\left[{}\begin{matrix}x=0\left(loại\right)\\x=-2\left(nhận\right)\end{matrix}\right.\)
=>x=-2
b: \(1+\dfrac{x+4}{5}< =x-\dfrac{x+3}{3}\)
=>\(\dfrac{5+x+4}{5}< =\dfrac{3x-x-3}{3}\)
=>\(\dfrac{x+9}{5}< =\dfrac{2x-3}{3}\)
=>\(3\left(x+9\right)< =5\left(2x-3\right)\)
=>\(3x+27< =10x-15\)
=>\(3x-10x< =-15-27\)
=>-7x<=-42
=>7x>=42
=>\(x>=\dfrac{42}{7}=6\)
