How to solve (x)^(2)-5x+6/x-2

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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$${ x }^{ 2 } -5x+6/x-2$$

$x^{2}-5x-2+\frac{6}{x}$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x^{2}-5x-2$ times $\frac{x}{x}$.

$$\frac{\left(x^{2}-5x-2\right)x}{x}+\frac{6}{x}$$

Since $\frac{\left(x^{2}-5x-2\right)x}{x}$ and $\frac{6}{x}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-5x-2\right)x+6}{x}$$

Do the multiplications in $\left(x^{2}-5x-2\right)x+6$.

$$\frac{x^{3}-5x^{2}-2x+6}{x}$$

$\frac{\left(x-1\right)\left(x-\left(2-\sqrt{10}\right)\right)\left(x-\left(\sqrt{10}+2\right)\right)}{x}$