Упростите выражение: 1) \(\frac{y^2-4}{7y} \cdot \frac{14}{y^2-4}\) 2) \(\frac{y^2-3y}{25-y^2} - \frac{7y-25}{25-y^2}\) 3) \(\frac{9p+5}{3p+6} + \frac{10p-12}{3p+6} + \frac{9p-1}{3p+6}\) Выполните действия: 4) \(\frac{7x+5}{3-x} + \frac{5x+11}{x-3}\) 5) \(\frac{(3a-1)^2}{4a-4} + \frac{(a-3)^2}{4-4a}\) 6) \(\frac{x^2-3x}{(2-x)^2} - \frac{x-4}{(x-2)^2}\) 7) \(\frac{7}{a-2} - \frac{b}{2-a}\) 8) \(\frac{6a}{5-a} - \frac{4a}{a-5}\)

Решение: 1) \(\frac{y^2-4}{7y} \cdot \frac{14}{y^2-4} = \frac{(y^2-4) \cdot 14}{7y \cdot (y^2-4)} = \frac{14}{7y} = \frac{2}{y}\) 2) \(\frac{y^2-3y}{25-y^2} - \frac{7y-25}{25-y^2} = \frac{y^2-3y-(7y-25)}{25-y^2} = \frac{y^2-3y-7y+25}{25-y^2} = \frac{y^2-10y+25}{25-y^2} = \frac{(y-5)^2}{(5-y)(5+y)} = \frac{-(5-y)^2}{(5-y)(5+y)} = -\frac{5-y}{5+y} = \frac{y-5}{y+5}\) 3) \(\frac{9p+5}{3p+6} + \frac{10p-12}{3p+6} + \frac{9p-1}{3p+6} = \frac{9p+5+10p-12+9p-1}{3p+6} = \frac{28p-8}{3p+6} = \frac{4(7p-2)}{3(p+2)}\) 4) \(\frac{7x+5}{3-x} + \frac{5x+11}{x-3} = \frac{7x+5}{3-x} - \frac{5x+11}{3-x} = \frac{7x+5-(5x+11)}{3-x} = \frac{7x+5-5x-11}{3-x} = \frac{2x-6}{3-x} = \frac{2(x-3)}{3-x} = -2\) 5) \(\frac{(3a-1)^2}{4a-4} + \frac{(a-3)^2}{4-4a} = \frac{(3a-1)^2}{4(a-1)} - \frac{(a-3)^2}{4(a-1)} = \frac{(3a-1)^2 - (a-3)^2}{4(a-1)} = \frac{(9a^2-6a+1) - (a^2-6a+9)}{4(a-1)} = \frac{8a^2-8}{4(a-1)} = \frac{8(a^2-1)}{4(a-1)} = \frac{2(a-1)(a+1)}{a-1} = 2(a+1)\) 6) \(\frac{x^2-3x}{(2-x)^2} - \frac{x-4}{(x-2)^2} = \frac{x^2-3x}{(2-x)^2} - \frac{x-4}{(2-x)^2} = \frac{x^2-3x-(x-4)}{(2-x)^2} = \frac{x^2-3x-x+4}{(2-x)^2} = \frac{x^2-4x+4}{(2-x)^2} = \frac{(x-2)^2}{(2-x)^2} = 1\) 7) \(\frac{7}{a-2} - \frac{b}{2-a} = \frac{7}{a-2} + \frac{b}{a-2} = \frac{7+b}{a-2}\) 8) \(\frac{6a}{5-a} - \frac{4a}{a-5} = \frac{6a}{5-a} + \frac{4a}{5-a} = \frac{6a+4a}{5-a} = \frac{10a}{5-a}\) Ответы: 1) \(\frac{2}{y}\) 2) \(\frac{y-5}{y+5}\) 3) \(\frac{4(7p-2)}{3(p+2)}\) 4) -2 5) 2(a+1) 6) 1 7) \(\frac{7+b}{a-2}\) 8) \(\frac{10a}{5-a}\)