question 22\nfind the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify…

question 22\nfind the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.\n$f(x)=\frac{5}{x}$\nquestion help: written example\nsubmit question

question 22\nfind the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.\n$f(x)=\frac{5}{x}$\nquestion help: written example\nsubmit question

Answer

Explanation:

Step1: Find (f(x + h))

Given (f(x)=\frac{5}{x}), then (f(x + h)=\frac{5}{x + h})

Step2: Substitute into difference - quotient formula

(\frac{f(x + h)-f(x)}{h}=\frac{\frac{5}{x + h}-\frac{5}{x}}{h})

Step3: Get a common denominator for the numerator

(\frac{\frac{5x-5(x + h)}{x(x + h)}}{h}=\frac{\frac{5x-5x-5h}{x(x + h)}}{h})

Step4: Simplify the numerator

(\frac{\frac{- 5h}{x(x + h)}}{h})

Step5: Divide by (h)

(\frac{-5h}{x(x + h)}\times\frac{1}{h}=-\frac{5}{x(x + h)})

Answer:

(-\frac{5}{x(x + h)})