g(u)=3/(u-2) sederhanakan ke [g(x+h)-g(x)]/h Tolong ya we.....

[tex]g(u) = \frac{3}{u-2} \\ \\ g(x+h) = \frac{3}{x + h -2} \\ \\ g(x) = \frac{3}{x - 2} \\ \\ [/tex]

Jawab:

[tex]\frac{g(x+h)-g(x)}{h} = \left( \frac{3}{x+h-2} - \frac{3}{x - 2} \right )\frac{1}{h} \\ \\ = \frac{3(x-2) - 3(x+h-2)}{(x+h-2)(x-2)} \frac{1}{h} \\ \\ = \frac{3x - 6 - 3x - 3h + 6}{(x+h-2)(x-2)} \frac{1}{h} \\ \\ = \frac{-3}{(x+h-2)(x-2)} \\ \\ = \frac{-3}{x^2+(h-4)x-2h+4}[/tex]