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## Homework Statement

*Find an equation of the tangent line to the curve at the given point.*

[tex]y = \frac{x - 1}{x - 2}[/tex] , (3, 2)

## Homework Equations

[tex]m = \lim_{h\to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex]y = mx + b[/tex]

## The Attempt at a Solution

[tex]\lim_{h\to 0} \frac{\frac{(x + h) - 1}{(x + h) - 2} - \frac{x - 1}{x - 2}}{h}[/tex]

[tex]\lim_{h\to 0} \frac{\frac{2 + h}{1 + h} - \frac{2}{1}}{h}[/tex]

[tex]\lim_{h\to 0} \frac{2 + h}{h + h^2} - \frac{2}{h}[/tex]

[tex]\lim_{h\to 0} \frac{2 + h}{h + h^2} - \frac{2 + 2h}{h + h^2}[/tex]

[tex]\lim_{h\to 0} \frac{h + 2h}{h + h^2}[/tex]

I'm not sure what to do after this step. The final answer is [tex]y = -x + 5[/tex]

Thanks.

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