Вариант 2 Упростите выражение: a) $$y + \frac{3y}{y-3}$$ b) $$\frac{2}{x-5} + \frac{x+5}{5x}$$ v) $$\frac{4}{x+4} - \frac{x}{x-4}$$ g) $$\frac{2p-q}{p^2+pq} + \frac{p-2q}{pq+q^2}$$

a) $$y + \frac{3y}{y-3} = \frac{y(y-3) + 3y}{y-3} = \frac{y^2 - 3y + 3y}{y-3} = \frac{y^2}{y-3}$$ b) $$\frac{2}{x-5} + \frac{x+5}{5x} = \frac{2(5x) + (x+5)(x-5)}{5x(x-5)} = \frac{10x + x^2 - 25}{5x(x-5)} = \frac{x^2 + 10x - 25}{5x(x-5)}$$ v) $$\frac{4}{x+4} - \frac{x}{x-4} = \frac{4(x-4) - x(x+4)}{(x+4)(x-4)} = \frac{4x - 16 - x^2 - 4x}{(x+4)(x-4)} = \frac{-x^2 - 16}{x^2 - 16} = -\frac{x^2 + 16}{x^2 - 16}$$ g) $$\frac{2p-q}{p^2+pq} + \frac{p-2q}{pq+q^2} = \frac{2p-q}{p(p+q)} + \frac{p-2q}{q(p+q)} = \frac{q(2p-q) + p(p-2q)}{pq(p+q)} = \frac{2pq - q^2 + p^2 - 2pq}{pq(p+q)} = \frac{p^2 - q^2}{pq(p+q)} = \frac{(p-q)(p+q)}{pq(p+q)} = \frac{p-q}{pq}$$