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

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