find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h\neq0$ for the given…

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h\neq0$ for the given function.\n$f(x)=\frac{6}{x}$\n$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h\neq0$ for the given function.\n$f(x)=\frac{6}{x}$\n$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Answer

Explanation:

Step1: Find f(x + h)

Given (f(x)=\frac{6}{x}), then (f(x + h)=\frac{6}{x + h})

Step2: Substitute into the difference - quotient formula

(\frac{f(x + h)-f(x)}{h}=\frac{\frac{6}{x + h}-\frac{6}{x}}{h})

Step3: Get a common denominator for the numerator

(\frac{\frac{6x-6(x + h)}{x(x + h)}}{h}=\frac{6x-6x-6h}{x(x + h)h})

Step4: Simplify the numerator

(\frac{- 6h}{x(x + h)h})

Step5: Cancel out the h terms

(\frac{-6}{x(x + h)})

Answer:

(\frac{-6}{x(x + h)})