Question

даю 20 балов срочно спростить уравнение

Answer 1

Ответ:

1) 2          2) -2          3) $\frac{a+1}{2}$           4) 1

Объяснение:

1)

$\frac{x-4}{x-2} -\frac{x}{2-x} \\\\\frac{x-4}{x-2} -\frac{x}{-(x-2)}\\\\\frac{x-4}{x-2} +\frac{x}{x-2}\\\\\frac{x-4+x}{x-2}\\\\\frac{2x-4}{x-2} \\\\\frac{2(x-2)}{x-2}$

Ответ: $2$

2)

$\frac{5x+6}{5-x} +\frac{3x+16}{x-5} \\\\\frac{5x+6}{-(x-5)} +\frac{3x+16}{x-5}\\\\-\frac{5x+6}{x-5} +\frac{3x+16}{x-5}\\\\\frac{-5x-6+3x+16}{x-5} \\\\\frac{-2x+10}{x-5} \\\\\frac{-2(x-5)}{x-5}$

Ответ: $-2$

3)

$\frac{(2a-1)^{2}}{6a-6} +\frac{(a-2)^{2}}{6-6a} \\\\\frac{(2a-1)^{2}}{6a-6} +\frac{(a-2)^{2}}{-(6a-6)}\\\\\frac{(2a-1)^{2}}{6a-6} -\frac{(a-2)^{2}}{6a-6}\\\\\frac{4a^{2}-4a+1-(a^{2}-4a+4)}{6a-6} \\\\\frac{4a^{2}-4a+1-a^{2}+4a-4}{6a-6}\\\\\frac{3a^{2}-3}{3*2(a-1)} \\\\\frac{3(a^{2}-1)}{3*2(a-1)} \\\\\frac{(a-1)(a+1)}{2(a-1)}$

Ответ: $\frac{a+1}{2}$

4)

$\frac{16-7x}{(x-4)^{2}} -\frac{x-x^{2}}{(4-x)^{2}}\\\\ \frac{16-7x}{(x-4)^{2}} -\frac{x-x^{2}}{(-(x-4))^{2}}\\\\\frac{16-7x}{(x-4)^{2}} -\frac{x-x^{2}}{(x-4)^{2}}\\\\\frac{16-7x-(x-x^{2})}{(x-4)^{2}} \\\\\frac{16-7x-x+x^{2}}{(x-4)^{2}}\\\\\frac{16-8x+x^{2}}{(x-4)^{2}}\\\\\frac{(4-x)^{2}}{(x-4)^{2}} \\\\\frac{(-(x-4))^{2}}{(x-4)^{2}}\\\\\frac{(x-4)^{2}}{(x-4)^{2}}$

Ответ: $1$