Question

Решите дробные рациональные уравнения
1. 2у-2/у+3 + у+3/у-3=5
2. 1/х-1 + 1/х^2-1=5/8

Answer 1

1) y1=-6; y2=5

2) x1=7/5; x2=3

Объяснение:

1) $\frac{2y-2}{y+3}+\frac{y+3}{y-3} =5\\\\ \frac{2y^{2}-8y+6+y^{2}+6y+9-5y^{2} +45}{(y+3)(y-3)} =0\\ \\ \frac{-2y^{2}-2y+60}{(y+3)(y-3)} =0\\\\ \frac{y^{2}+y-30}{(y+3)(y-3)} =0\\\\ (y+6)(y-5)=0\\y=-6; y=5\\(y+3)(y-3) \neq 0\\y\neq 3; y\neq -3$

2)  $\frac{1}{x-1} +\frac{1}{x^{2} -1} =\frac{5}{8} \\\\ \frac{8x+8+8-5x^{2}+5 }{8(x+1)(x-1)} =0\\\\ \frac{-5x^{2}+8x+21 }{8(x+1)(x-1)} =0\\ \\x\neq1; x\neq -1\\ 5x^{2} -8x-21=0\\(5x+7)(x-3)=0\\x1=-\frac{7}{5}; x2=3$