Bonjour,
[tex]A(x) = \frac{1}{x+1} -\frac{3}{2} \\\\=\frac{2*1}{2(x+1)} -\frac{(x+1)*3}{(x+1)*2} \\\\=\frac{2-3x-3}{2x+2}\\\\=\frac{-3x-1}{2x+2}[/tex]
[tex]B(x) = \frac{x}{x+3} +\frac{3}{-x+1} \\\\=\frac{x(-x+1)}{(x+3)(-x+1)} +\frac{3(x+3)}{(-x+1)(x+3)} \\\\=\frac{-x^{2}+x+3x+9 }{-x^{2} +x-3x+3} \\\\=\frac{-x^{2}+4x+9 }{-x^{2} -2x+3}[/tex]
