Answer:
6.
[tex] \frac{4}{x {}^{2} - 8x + 12 }= \frac{x}{x - 2} + \frac{1}{x - 6} \\ \frac{4}{(x - 6)(x - 2)} = \frac{x}{x - 2} + \frac{1}{x - 6} \\ \frac{4(x - 6)(x - 2)}{(x - 6)(x - 2)} = \frac{x(x - 6)(x - 2)}{x - 2} + \frac{1(x - 6)(x - 2)}{x - 6} \\ 4 = x(x - 6) +(x - 2) \\ 4 = x {}^{2} - 6x + x - 2 \\ x {}^{2} - 5x - 6 = 0 \\ (x - 6)(x + 1) = 0 \\ \\ x = 6 \: \: \: \: \: \: \: \: \: \:x = - 1[/tex]
7.
[tex] \frac{5}{x + 2} = \frac{1}{x - 4} \\ \frac{5(x + 2)(x - 4)}{x + 2} = \frac{1(x + 2)(x - 4)}{x - 4} \\5x - 20 = x +2 \\ 4x = 22 \\ x = \frac{11}{2} [/tex]
8.
[tex]x - 8 = - \frac{15}{x} \\ x - 8(x) = - \frac{15(x)}{x} \\ x {}^{2} - 8x = - 15 \\ x {}^{2} - 8x + 15 = 0 \\ (x - 5)(x - 3) = 0 \\ \\ x = 5 \: \: \: \: \: \: \: \: \: \: x = 3[/tex]
