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[latex]1) \frac{5b}{14} + \frac{9b}{14}=\frac{14b}{14}=b \\ 2) \frac{9m}{7n} - \frac{2m}{7n}=\frac{7m}{7n}=\frac{m}{n} \\ 3) \frac{5x-3y}{8z} + \frac{3x-13y}{8z} =\frac{8x-16y}{8z}=\frac{8(x-2y)}{8z}=\frac{x-2y}{z} \\ \\ 1) \frac{3}{m} + \frac{5}{n} =\frac{3n+5m}{mn} \\ 2) \frac{4}{x} - \frac{3}{xy} = \frac{4y-3}{xy} \\ 3) \frac{7}{9ab}- \frac{13}{12ab}= \frac{28-39}{36ab}=-\frac{11}{36ab} \\ \\1)\frac{x+4}{2(x-3)}-\frac{x+1}{x-3} =\frac{x+4-2x-2}{2(x-3)}=\frac{2-x}{2(x-3)}[/latex]
[latex]2)\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)}=[/latex][latex]\frac{2a+21}{15(a-1)} \\ 3) \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)} =[/latex][latex]\frac{16x+20}{(x-5)(x+5)} =\frac{4(4x+5)}{(x-5)(x+5)} \\ 4) \frac{4b}{3b-21}+ \frac{3b}{14-2b} =\frac{4b}{3(b-7)}+ \frac{3b}{2(7-b)} =\frac{4b}{3(b-7)}- \frac{3b}{2(b-7)} =\frac{8b-9b}{6(b-7)} =[/latex][latex]-\frac{b}{6(b-7)}=\frac{b}{6(7-b)}[/latex]
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