Simplify (F(x+h)-Fx)/h

Problem

(F*(x+h)−F(x))/h

Solution

1. Identify the expression as the difference quotient, which is used to find the derivative of a function F(x) using the limit definition.

2. Interpret the task as a request to simplify the general form of the difference quotient, which represents the average rate of change of the function F over the interval [x,x+h]

3. Observe that without a specific definition for the function F(x) the expression cannot be reduced further into a specific algebraic result.

4. Conclude that the expression is already in its most simplified general form for an arbitrary function F

Final Answer

(F*(x+h)−F(x))/h=(F*(x+h)−F(x))/h

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