Question

3-1/x²-1+10/1+x²=6/9

Answer 1

$3-frac{1}{x^{2}-1}+frac{10}{1+x^{2}}=frac{6}{9}\\3-frac{1}{x^{2}-1}+frac{10}{x^{2}+1}-frac{2}{3}=0\\frac{9x^{4}-9-3x^{2}-3+30x^{2} -30-2x^{4}+2}{3(x^{2}-1)(x^{2}+1)}=0\\frac{7x^{4}+27x^{2}-40}{3(x^{2}-1)(x^{2}+1)}=0 \\7x^{4} +27x^{2}-40=0;xneq-1;xneq1$

Сделаем замену : x² = m , m  ≥ 0

7m² + 27m -40 = 0

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

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