Ты просишь упростить алгебраические выражения.

Конечно, давай упростим выражения! **1. Упростите выражение:** а) $\frac{3c + a}{4c} - \frac{a - 7c}{4c} = \frac{3c + a - a + 7c}{4c} = \frac{10c}{4c} = \frac{5}{2}$ б) $\frac{2p}{p + 3} + \frac{3 - p}{p + 3} = \frac{2p + 3 - p}{p + 3} = \frac{p + 3}{p + 3} = 1$ в) $\frac{x^2}{x - 4} + \frac{4x}{4 - x} = \frac{x^2}{x - 4} - \frac{4x}{x - 4} = \frac{x^2 - 4x}{x - 4} = \frac{x(x - 4)}{x - 4} = x$ г) $\frac{m}{m^2 - n^2} - \frac{n}{m^2 - n^2} = \frac{m - n}{m^2 - n^2} = \frac{m - n}{(m - n)(m + n)} = \frac{1}{m + n}$ **2. Упростите выражение:** а) $y + \frac{3y}{y - 3} = \frac{y(y - 3) + 3y}{y - 3} = \frac{y^2 - 3y + 3y}{y - 3} = \frac{y^2}{y - 3}$ б) $\frac{2}{x - 5} + \frac{x + 5}{5x} = \frac{2 \cdot 5x + (x + 5)(x - 5)}{5x(x - 5)} = \frac{10x + x^2 - 25}{5x(x - 5)} = \frac{x^2 + 10x - 25}{5x(x - 5)}$ в) $\frac{4}{x + 4} - \frac{x}{x - 4} = \frac{4(x - 4) - x(x + 4)}{(x + 4)(x - 4)} = \frac{4x - 16 - x^2 - 4x}{(x + 4)(x - 4)} = \frac{-x^2 - 16}{(x + 4)(x - 4)} = -\frac{x^2 + 16}{x^2 - 16}$ г) $\frac{2p - q}{p^2 + pq} + \frac{p - 2q}{pq + q^2} = \frac{2p - q}{p(p + q)} + \frac{p - 2q}{q(p + q)} = \frac{q(2p - q) + p(p - 2q)}{pq(p + q)} = \frac{2pq - q^2 + p^2 - 2pq}{pq(p + q)} = \frac{p^2 - q^2}{pq(p + q)} = \frac{(p - q)(p + q)}{pq(p + q)} = \frac{p - q}{pq}$ **3. Упростите выражение:** а) $\frac{5}{x^2 + 5x} + \frac{x + 15}{25 - x^2} = \frac{5}{x(x + 5)} - \frac{x + 15}{(x - 5)(x + 5)} = \frac{5(x - 5) - x(x + 15)}{x(x - 5)(x + 5)} = \frac{5x - 25 - x^2 - 15x}{x(x - 5)(x + 5)} = \frac{-x^2 - 10x - 25}{x(x - 5)(x + 5)} = -\frac{(x + 5)^2}{x(x - 5)(x + 5)} = -\frac{x + 5}{x(x - 5)}$ б) $\frac{1}{x + 3} + \frac{9x}{x^3 + 27} = \frac{1}{x + 3} + \frac{9x}{(x + 3)(x^2 - 3x + 9)} = \frac{x^2 - 3x + 9 + 9x}{(x + 3)(x^2 - 3x + 9)} = \frac{x^2 + 6x + 9}{(x + 3)(x^2 - 3x + 9)} = \frac{(x + 3)^2}{(x + 3)(x^2 - 3x + 9)} = \frac{x + 3}{x^2 - 3x + 9}$ в) $\frac{2}{x} + \frac{12}{x^2 - 6x} - \frac{1 - x}{x - 6} = \frac{2}{x} + \frac{12}{x(x - 6)} - \frac{1 - x}{x - 6} = \frac{2(x - 6) + 12 - x(1 - x)}{x(x - 6)} = \frac{2x - 12 + 12 - x + x^2}{x(x - 6)} = \frac{x^2 + x}{x(x - 6)} = \frac{x(x + 1)}{x(x - 6)} = \frac{x + 1}{x - 6}$