Question

Дам 60 баллов.
1/х-4 - 1/х+4 = 1/х-5 - 1/х-2

Answer 1

$\displaystyle\bf\\\frac{1}{x-4} -\frac{1}{x+4} =\frac{1}{x-5} -\frac{1}{x-2} \\\\\\\frac{x+4-x+4}{(x-4)(x+4)}=\frac{x-2-x+5}{(x-5)(x-2)} \\\\\\\frac{8}{(x-4)(x+4)}=\frac{3}{(x-5)(x-2)} \\\\\\8\cdot(x-5)\cdot(x-2)=3\cdot(x-4)(x+4)\\\\\\8\cdot(x^{2} -2x-5x+10)=3\cdot(x^{2} -16)\\\\\\8\cdot(x^{2} -7x+10)=3\cdot(x^{2} -16)\\\\\\8x^{2} -56x+80=3x^{2} -48\\\\\\8x^{2} -56x+80-3x^{2} +48=0\\\\\\5x^{2}-56x+128=0\\\\\\D=(-56)^{2} -4\cdot 5\cdot 128=3136-2560=576=24^{2}$

$\displaystyle\bf\\x_{1} =\frac{56-24}{10} =\frac{32}{10} =3,2\\\\\\x_{2} =\frac{56+24}{10} =\frac{80}{10} =8\\\\\\Otvet \ : \ 3,2 \ \ ; \ \ 8$