Question

Решите пожалуйста даю 40 баллов полный ответ

Answer 1

$1)\frac{2}{x-6} =-5\\2)\frac{8}{x-3}+ \frac{3}{x-8} =2$

1) Перенесем -5 вправо:
$\frac{2}{x - 6} - ( - 5) = 0 \\ \frac{2}{x - 6} + 5 = 0$
Внесем 5 в дробь
$\frac{2 + 5(x - 6)}{x - 6} = 0 \\ \frac{2 + 5x - 30}{x - 6} = 0$
x не равен 6
$5x - 28 = 0 \\ x = \frac{28}{5} = 5.6$
2)
$\frac{8}{x - 3} + \frac{3}{x - 8} = 2 \\ \frac{8(x - 8) + 3(x - 3)}{(x - 3)(x - 8)} = 2 \\ \frac{8(x - 8) + 3(x - 3) - 2(x - 3)(x - 8)}{(x - 3)(x - 8)} = 0 \\ 8x -64 + 3x - 9 - 2( {x}^{2} - 11x + 24) = 0 \\ 11x - 73 - 2 {x}^{2} + 22x - 48 = 0 \\ - 2 {x}^{2} + 33x - 121 = 0 \\ 2 {x}^{2} - 33x + 121 = 0$
$x = \frac{11}{2} = 5.5 \\ x = 11$

Answer 2

1)$\displaystyle \frac{2}{x-6} =-5;\\\frac{x-6}{2} = -\frac{1}{5};\\5x-30=-2;\\5x=28;\\x=5,6;$

2)$\displaystyle \frac{8}{x-3}+ \frac{3}{x-8} =2;\\\frac{8(x-8)+3(x-3)}{(x-8)(x-3)}=2;\\8x-64+3x-9=2(x-8)(x-3);\\11x-73=2x^2-22x+48;\\-2x^2+33x-121=0;$

D=33²-4*2*121=121;

x=(-33-11)/-4=11;

x=(-33+11)/-4=5,5;