Question

х-7/х-2+х+4/х+2=1
а)ОДЗ
Б) определите объщий знаменател
в) решите уравнение​

Answer 1

$\displaystyle\bf\\\frac{x-7}{x-2}+ \frac{x+4}{x+2} =1\\\\1) \ \ ODZ \ : \ \ x\neq 2 \ \ ; \ \ x\neq -2\\\\2) \ \ (x-2)(x+2)\\\\3)\\\\\frac{x-7}{x-2}+ \frac{x+4}{x+2} =1\\\\\\\frac{x-7}{x-2}+ \frac{x+4}{x+2} -1=0\\\\\\\frac{(x-7)\cdot(x+2)+(x+4)\cdot(x-2)-(x-2)\cdot(x+2)}{(x-2)(x+2)} =0\\\\\\\frac{x^{2} +2x-7x-14+x^{2} -2x+4x-8-x^{2} +4}{(x-2)(x+2)} =0\\\\\\\frac{x^{2} -3x-18}{(x-2)(x+2)} =0\\\\\\x^{2} -3x-18=0\\\\D=(-3)^{2} -4\cdot(-18)=9+72=81=9^{2}$

$\displaystyle\bf\\x_{1} =\frac{3+9}{2} =6\\\\\\x_{2} =\frac{3-9}{2} =-3\\\\\\Otvet:6 \ ; \ -3$