Question

Please help! Assuming that h is not equal to zero, compute and simplify the difference quotient for f(x)=(x-4)/(2-x)

Answer 1

Difference quotient is just like slope formula.
\[\large m=\frac{y_2-y_2}{x_2-x_1}\]
Where y_2 = f(x+h), y_1 = f(x), and x_2 - x_1 = h.

Answer 2

\[\frac{ f(x+h)-f(x) }{ h }\]
\[\frac{ \frac{ x+h-4 }{ 2-(x+h) }-\frac{ x-4 }{ 2-x } }{h }\]
simplify