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$f(x)=\frac{13}{x}$\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$f(x)=\frac{13}{x}$\n$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Answer

Explanation:

Step1: Find (f(x + h))

Substitute (x+h) into (f(x)): (f(x + h)=\frac{13}{x + h})

Step2: Calculate (f(x + h)-f(x))

(f(x + h)-f(x)=\frac{13}{x + h}-\frac{13}{x}=\frac{13x-13(x + h)}{x(x + h)}=\frac{13x-13x-13h}{x(x + h)}=\frac{- 13h}{x(x + h)})

Step3: Divide by (h)

(\frac{f(x + h)-f(x)}{h}=\frac{\frac{-13h}{x(x + h)}}{h}=\frac{-13h}{x(x + h)}\times\frac{1}{h}=-\frac{13}{x(x + h)})

Answer:

(-\frac{13}{x(x + h)})