Question

$frac{ x+4}{2x-6} -frac{x+1}{x-3} frac{a+3}{3a-3} +frac{2-a}{5a-5} frac{x+5}{x-5}-frac{x-1}{x+5}$

Answer 1

$displaystyle a). frac{x+4}{2x-6}-frac{x+1}{x-3}=frac{x+4}{2(x-3)}-frac{x+1}{x-3}=frac{x+4-2(x+1)}{2(x-3)}=frac{2-x}{2x-6};\\\b). frac{a+3}{3a-3}+frac{2-a}{5a-5}=frac{a+3}{3(a-1)}+frac{2-a}{5(a-1)}=frac{5(a+3)+3(2-a)}{15(a-1)}=\\\=frac{5a+15+6-3a}{15(a-1)}=frac{2a+21}{15a-15};\\\c). frac{x+5}{x-5}-frac{x-1}{x+5}=frac{(x+5)^{2}-(x-1)(x-5)}{(x-5)(x+5)}=\\\=frac{x^{2}+10x+25-x^{2}+6x-5}{(x-5)(x+5)}=frac{16x+20}{x^{2}-25};$