Find the equation of the tangent to the curve (y = frac{x - 1}{2x +

Explanation

\(y = \frac{x - 1}{2x + 1}, x \neq -\frac{1}{2}\)

Using the quotient rule, we have

\(\frac{\mathrm d y}{\mathrm d x} = \frac{(2x + 1). 1 - (x - 1). 2}{(2x - 1)^{2}}\)

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

\(\frac{\mathrm d y}{\mathrm d x} = \frac{3}{(2x + 1)^{2}}\)

At (1, 0), \(\frac{\mathrm d y}{\mathrm d x} = \frac{3}{(2(1) + 1)^{2}} = \frac{3}{9} = \frac{1}{3}\)

Equation : \(\frac{y - 0}{x - 1} = \frac{1}{3}\)

\(y = \frac{1}{3}(x - 1)\)