Question

3-1/x²-1+10/1+x²=6/9

Answer 1

$3-\frac{1}{x^{2}-1}+\frac{10}{1+x^{2}}=\frac{6}{9}\\\\3-\frac{1}{x^{2}-1}+\frac{10}{x^{2}+1}-\frac{2}{3}=0\\\\\frac{9x^{4}-9-3x^{2}-3+30x^{2} -30-2x^{4}+2}{3(x^{2}-1)(x^{2}+1)}=0\\\\\frac{7x^{4}+27x^{2}-40}{3(x^{2}-1)(x^{2}+1)}=0 \\\\7x^{4} +27x^{2}-40=0;x\neq-1;x\neq1$

Сделаем замену : x² = m , m  ≥ 0

7m² + 27m -40 = 0

D = 27² - 4 * 7 * (-40) = 729 + 1120 = 1849 = 43²

$m_{1}=\frac{-27+43}{14}=\frac{16}{14}=\frac{8}{7}\\\\m_{2}=\frac{-27-43}{14}=-\frac{70}{14}=-5<0-neyd\\\\x^{2}=\frac{8}{7}\\\\x_{1,2}=\pm\sqrt{\frac{8}{7}}=\pm\frac{2\sqrt{2} }{\sqrt{7}}=\pm\frac{2\sqrt{14}}{7}$