3x2−5x−1=0. 1/x - 1/(x+2) = 1/3 show that it reduces to x2+2x−6=0. x2+2x−6=0. 2x2−3x−7=0.

To combine $\frac{1}{x} - \frac{1}{x+2}$, find a common denominator, which is $x(x+2)$.

$$\frac{1(x+2)}{x(x+2)} - \frac{1(x)}{x(x+2)} = \frac{1}{3}$$ $$\frac{x+2-x}{x(x+2)} = \frac{1}{3}$$ $$\frac{2}{x(x+2)} = \frac{1}{3}$$

Multiply both sides by $3x(x+2)$:

$$2 \times 3 = 1 \times x(x+2)$$ $$6 = x(x+2)$$

$$6 = x^2 + 2x$$

Subtract 6 from both sides to set the equation to zero:

$$0 = x^2 + 2x - 6$$ $$x^2 + 2x - 6 = 0$$

The derived equation $x^2 + 2x - 6 = 0$ matches the target equation.

Therefore, it is shown that the equation $\frac{1}{x} - \frac{1}{x+2} = \frac{1}{3}$ reduces to $\boxed{x^2+2x-6=0}$.