Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 213

$$1)y=\frac{1+\cos x}{\sin x};$$

$$=\frac{-{\sin }^{2}x-\cos x-{\cos }^{2}x}{{\sin }^{2}x}=$$

$$=\frac{-(1+\cos x)}{1-{\cos }^{2}x}=\frac{-1}{1-\cos x}=$$

$$=\frac{1}{\cos x-1}.$$

$$2)y=\frac{\sqrt{3x}}{3^x+1};$$

$$=\frac{\sqrt{3}}{2\sqrt{x}\bullet (3^x+1)}-\frac{\sqrt{3x}\bullet 3^x\bullet \ln 3}{{(3^x+1)}^2}.$$

$$3)y=\frac{x^2-2x+3}{x^2+4x+1};$$

$$=\frac{6x^2-4x-14}{{(x^2+4x+1)}^2}=$$

$$=\frac{2(3x^2-2x-7)}{{(x^2+4x+1)}^2}.$$

$$4)y=\frac{x^2-x+1}{x^2+x+1};$$

$$=\frac{2x^2-2}{{(x^2+x+1)}^2}=\frac{2(x^2-1)}{{(x^2+x+1)}^2}.$$