16) 1 / (m-1) + m / (1-m) =

16) $\frac{1}{m-1} + \frac{m}{1-m} = \frac{1}{m-1} - \frac{m}{m-1} = \frac{1-m}{m-1} = -1$ 17) $\frac{a^2}{a+3} : \frac{2a}{a+3} = \frac{a^2}{a+3} \cdot \frac{a+3}{2a} = \frac{a^2}{2a} = \frac{a}{2}$ 18) $\frac{(a+3)^2}{2x^2} \cdot \frac{x}{a+3} = \frac{(a+3) \cdot x}{2x^2} = \frac{a+3}{2x}$ 19) $\frac{n^2}{9a} + \frac{n^2}{3a} = \frac{n^2}{9a} + \frac{3n^2}{9a} = \frac{4n^2}{9a}$ 20) $\frac{a+3}{a-7} \cdot \frac{7-a}{a+3} = \frac{7-a}{a-7} = \frac{-(a-7)}{a-7} = -1$ 21) $\frac{3x^2}{5y} : \frac{9x}{25y} = \frac{3x^2}{5y} \cdot \frac{25y}{9x} = \frac{3x^2 \cdot 25y}{5y \cdot 9x} = \frac{75x^2y}{45xy} = \frac{5x}{3}$ 22) $\frac{4(3a+1)}{a^2} - \frac{12}{a} = \frac{12a+4}{a^2} - \frac{12a}{a^2} = \frac{12a+4-12a}{a^2} = \frac{4}{a^2}$ 23) $\frac{2a}{a-6} + \frac{a+5}{6-a} = \frac{2a}{a-6} - \frac{a+5}{a-6} = \frac{2a-(a+5)}{a-6} = \frac{2a-a-5}{a-6} = \frac{a-5}{a-6}$ 24) $1 - \frac{a}{x} = \frac{x-a}{x}$ 25) $1 - \frac{1}{1+a} = \frac{1+a-1}{1+a} = \frac{a}{1+a}$ 26) $x + \frac{x}{3} = \frac{3x+x}{3} = \frac{4x}{3}$ 27) $\frac{x-4}{x} \cdot 3 = \frac{3x-12}{x}$ 28) $ax \cdot \frac{ax-1}{x} = a(ax-1) = a^2x - a$ 29) $(a-1) + \frac{a}{2} = \frac{2(a-1)+a}{2} = \frac{2a-2+a}{2} = \frac{3a-2}{2}$ 30) $\frac{x+2}{(x-2)^2} \cdot \frac{5(x-2)}{x+2} = \frac{5(x-2)}{(x-2)^2} = \frac{5}{x-2}$