Преоброзуйте в дробь выражение:[latex] \frac{x}{x-1} + \frac{x}{x+1} [/latex][latex] \frac{x}{x-2y} - \frac{4y ^{2} }{x ^{2}-2xy } [/latex][latex]2a+b - \frac{4ab}{2a+b} [/latex]Упростите выражение:[latex] \frac{3}{x+3} + \frac...

[latex] \frac{x}{x-1} + \frac{x}{x+1} = \frac{x(x+1)+x(x-1)}{(x-1)(x+1)}= \frac{x^2+x+x^2-x}{x^2-1}= \frac{2x^2}{x^2-1}[/latex] [latex] \frac{x}{x-2y} - \frac{4y ^{2} }{x ^{2}-2xy } = \frac{x^2}{x(x-2y)} - \frac{4y ^{2} }{x(x-2y) } = \frac{x^2-4y^2}{x(x-2y)} = \frac{(x-2y)(x+2y)}{x(x-2y)} = \frac{x+2y}{x} [/latex] [latex]2a+b - \frac{4ab}{2a+b} =\frac{(2a+b)^2-4ab}{2a+b} =\frac{4a^2+4ab+b^2-4ab}{2a+b} =\frac{4a^2+b^2}{2a+b} [/latex] [latex] \frac{3}{x+3} + \frac{3}{x^{2}-3x } + \frac{2x}{9-x^{2} } = \frac{3}{x+3} + \frac{3}{x(x-3) } - \frac{2x}{(x-3)(x+3) } = \\\ = \frac{3x(x-3)+3(x+3)-2x^2}{x(x+3)(x-3)}= \frac{3x^2-9x+3x+9-2x^2}{x(x+3)(x-3)}= \frac{x^2-6x+9}{x(x+3)(x-3)}= \\\ =\frac{(x-3)^2}{x(x+3)(x-3)}=\frac{x-3}{x(x+3)}[/latex]