Решите уравнения 1234 номера и все с полным решением

[latex]1)\quad \frac{3x^2-7}{x+7} =\frac{10x+1}{x+7}\\\\3x^2-7=10x+1\; ,\; \; \; x\ne -7\\\\3x^2-7-10x-1=0\\\\3x^2-10x-8=0\\\\D/4=25+24=49\; ,\; \; x_1=\frac{5-7}{3}=-\frac{2}{3} \; ,\; \; x_2= \frac{5+7}{3} =4\\\\2)\quad \frac{3x^2-7x}{x-3}= \frac{2x^2-6}{3-x} \; ,\; \; x\ne 3\\\\3x^2-7x=-(2x^2-6)\\\\5x^2-7x-6=0\\\\D=49+120=169\\\\x_1= \frac{7-13}{10}=-\frac{3}{5}\; , \; \; x_2=\frac{7+13}{10}=2[/latex] [latex]3)\quad \frac{y^3+y^2-12y}{(y-3)(y+2)}=0\; ,\; \; \; ODZ:\; \; y\ne 3\; ,\; y\ne -2\\\\ \frac{y(y^2+y-12)}{(y-3)(y+2)} =0\; \; \to \; \; \; y(y^2+y-12)=0\; ,\; y\ne 3\; ,\; y\ne -2\\\\y_1=0\\\\y^2+y-12=(y-3)(y+4)=0\; \; \to \; \; y_2=-4\; ,\; y_3=3\notin ODZ\\\\Otvet:\; \; y_1=0\; ,\; \; y_2=-4\; .\\\\4)\quad \frac{24}{x^2-4x} +\frac{4}{x^2+2x}-\frac{1}{x+2} =0\; ,\; \; \; ODZ:\; \; x\ne 0,\; x\ne 4,\; x\ne -2.\\\\ \frac{24}{x(x-4)}+\frac{4}{x(x+2)}-\frac{1}{x+2} =0[/latex] [latex]\frac{24(x+2)+4(x-4)-x(x-4)}{x(x-4)(x+2)} =0[/latex] [latex] \frac{24x+48+4x-16-x^2+4x}{x(x-4)(x+2)}=0\\\\\frac{-x^2+32x+32}{x(x-4)(x+2)}=0\\\\x^2-32x-32=0\\\\D/4=288\; ,\\\\x_1= 16-\sqrt{288}=16-12\sqrt2\\\\x_2=16+12\sqrt2[/latex]