Simplifying Difference Quotients with Variable Expressions - How to Solve?

[Niaboc67]

Homework Statement

Find f(a), f(a + h),and the difference quotient f(a + h) − f(a), h where h ≠ 0.

f(x) = 5x/x-1

f(a) = ?
f(a + h) = ?
f(a + h) − f(a)/(h) = ?

The Attempt at a Solution

As I understand it I must substitute the values but I don't understand the question. say if it were something like 1/x I would know to fill it into (1/(x+h)-1/x) / h
But this just confuses me I don't know how to answer these questions

 

[Ray Vickson]

Homework Statement

Find f(a), f(a + h),and the difference quotient f(a + h) − f(a), h where h ≠ 0.

f(x) = 5x/x-1

f(a) = ?
f(a + h) = ?
f(a + h) − f(a)/(h) = ?

The Attempt at a Solution

As I understand it I must substitute the values but I don't understand the question. say if it were something like 1/x I would know to fill it into (1/(x+h)-1/x) / h
But this just confuses me I don't know how to answer these questions

The way you wrote it you have
f(x) = \frac{5x}{x} - 1 = 5 - 1 = 4
so $f(a) = f(a+h) = 4$. Perhaps you really did not mean what you wrote, but because you failed to use parentheses it is impossible to say. And, of course, you wrote
f(a+h) - \frac{f(a)}{h} = 4 - \frac{4}{h}.
Again, maybe you meant something different.

 

[Niaboc67]

What I meant was: f(x) = (5x)/(x-1) my mistake

 

[haruspex]

What I meant was: f(x) = (5x)/(x-1) my mistake

Just replace every instance of x with the given value. Where the given value consists of an expression, like a+h, put the expression in parentheses when making the substitution.