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I'm having trouble understanding an example from my test and I would appreciate your help clarifying how to get from one step to the next.

Problem: Find an equation of the tangent line to the hyberola y = 3/x at the point (3,1)

Eqation: [tex] m = \frac{f(a+h) - f(a)}{h} [/tex]

[tex] m = \frac{f(3 + h) - f(3)}{h} [/tex]

[tex]= \frac{\frac {3}{3 + h} - 1}{h} [/tex]

[tex]= \frac{\frac {3 - (3 + h)}{3 + h}}{h} [/tex]

(I'm assuming here they have just converted 1 to 3 + h / 3 + h, but I don't understand how they get to the next step...)

[tex]

= \frac{-h}{h(3+ h)}[/tex]

[tex]= \frac{-1}{3 + h} [/tex]

[tex]= \frac{-1}{3}[/tex][/tex]