Find and simplify the difference quotient $$\frac { f ( a + h ) - f ( a ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = \frac { 7 } { x + 1 }$$
A) $\frac { - 7 } { a ( a + h ) }$
B) $\frac { - 7 } { a ( a + h + 1 ) }$
C) $\frac { - 7 } { ( a + 1 ) ( a + h + 1 ) }$
D) $\frac { - 7 } { ( a + 1 ) ( a + h ) }$

Question

Quizplus · Accepted Answer

To find the difference quotient, substitute $f(x) = \frac{7}{x+1}$ into the formula: $\frac{f(a+h)-f(a)}{h}$. This gives $\frac{\frac{7}{(a+h)+1} - \frac{7}{a+1}}{h}$. Simplifying this expression leads to $\frac{-7}{(a+1)(a+h+1)}$, which matches choice C.

Find and Simplify the Difference Quotient f(a+h)−f(a)h,h≠0\frac { f ( a + h ) - f ( a ) } { h } , h \neq 0hf(a+h)−f(a)​,h=0

Find and Simplify the Difference Quotient $\frac { f ( a + h ) - f ( a ) } { h } , h \neq 0$