Simplify the expression sqrt(100) - 72 / 24. Solve the equation (x+2)/(x+3) = (1)/(x-2). Given y = sqrt(x2 + 1), find (dy)/(dx).

$$10 - 3 = 7$$

The simplified expression is $\boxed{7}$.

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Solve the equation $\frac{x+2}{x+3} = \frac{1}{x-2}$.

$$x^2 - x - 4 - 3 = 0$$ $$x^2 - x - 7 = 0$$

Here, $a=1$, $b=-1$, $c=-7$.

$$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-7)}}{2(1)}$$ $$x = \frac{1 \pm \sqrt{1 + 28}}{2}$$ $$x = \frac{1 \pm \sqrt{29}}{2}$$

The solutions for $x$ are $\boxed{\frac{1 \pm \sqrt{29}}{2}}$.

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Given $y = \sqrt{x^2 + 1}$, find $\frac{dy}{dx}$.

Let $u = x^2 + 1$. Then $y = u^{1/2}$.
The derivative of $y$ with respect to $u$ is:

$$\frac{dy}{du} = \frac{1}{2} u^{-1/2}$$

The derivative of $u$ with respect to $x$ is:

$$\frac{du}{dx} = 2x$$

$$\frac{dy}{dx} = \frac{1}{2} (x^2 + 1)^{-1/2} \cdot (2x)$$ $$\frac{dy}{dx} = x (x^2 + 1)^{-1/2}$$

$$\frac{dy}{dx} = \frac{x}{\sqrt{x^2 + 1}}$$

The derivative is $\boxed{\frac{x}{\sqrt{x^2 + 1}}}$.

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Simplify the expression $y = \frac{x^2 - 3x + 2}{x^2 - 1}$.

We look for two numbers that multiply to 2 and add to -3. These numbers are -1 and -2.

$$x^2 - 3x + 2 = (x-1)(x-2)$$

This is a difference of squares, $a^2 - b^2 = (a-b)(a+b)$.

$$x^2 - 1 = (x-1)(x+1)$$

$$y = \frac{x-2}{x+1}$$

The simplified expression is $\boxed{\frac{x-2}{x+1}}$.