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$\frac{42x^3y^3}{28y^2y^4} = \frac{3x}{2y} \\\ \frac{x^2-2x}{x^2-4} = \frac{x(x-2)}{(x-2)(x+2)} = \frac{x}{x+2}$

$\frac{9m}{25n^2} = \frac{27m^2}{75mn^2} \\\\ \frac{4}{15mn} = \frac{20n}{75mn^2}$

$\frac{5m}{n} = \frac{5m(m-n)}{n(m-n)} \\\ \frac{n}{m-n} = \frac{n^2}{n(m-n)}$

$\frac{a}{a-5} = \frac{a(a+4)}{(a+4)(a-5)} \\\ \frac{3a}{a+4} = \frac{3a(a-5)}{(a+4)(a-5)}$

$\frac{4y}{4-y^2} = \frac{4y}{(2-y)(2+y)}= \frac{16y}{4(4-y^2)} \\\ \frac{1}{8+4y} = \frac{1}{4(2+y)} = \frac{2-y}{4(4-y^2)}$

$\frac{15x^5y^7}{25x^6y^6} = \frac{3y}{5x} \\\ \frac{a^2-25}{a^2-10a+25} = \frac{(a-5)(a+5)}{(a-5)^2} =\frac{a+5}{a-5}$

$\frac{2x}{14y^2z} = \frac{x^3}{7x^2y^2z} \\\ \frac{3y}{21x^2z} = \frac{y^3}{7x^2y^2z}$

$\frac{6+t}{6t} = \frac{(6+t)(2+t)}{6t(2+t)} \\\ \frac{4t}{6+3t} = \frac{8t^2}{6t(2+t)}$

$\frac{k}{k-1} = \frac{k(k-2)}{(k-1)(k-2)} \\\ \frac{k+1}{k-2} = \frac{(k+1)(k-1)}{(k-1)(k-2)} = \frac{k^2-1}{(k-1)(k-2)}$

$\frac{3a}{(3a+2)^2} = \frac{3a(3a-2)}{(3a-2)(3a+2)^2} \\\ \frac{3a+2}{9a^2-4} = \frac{(3a+2)^2}{(3a-2)(3a+2)^2}=$