Math  /  Algebra

QuestionCalculate the difference quotient f(x+h)f(x)h\frac{f(x+h)-f(x)}{h} for f(x)=4xx+3f(x)=\frac{4 x}{x+3}, where h0h \neq 0.

Studdy Solution
Now, we can cancel out hh from the numerator and the denominator.
f(x+h)f(x)h=12(x+h+3)(x+3)\frac{f(x+h)-f(x)}{h} = \frac{12}{(x+h+3)(x+3)}So, the difference quotient of f(x)=4xx+3f(x)=\frac{4 x}{x+3} is 12(x+h+3)(x+3)\frac{12}{(x+h+3)(x+3)}.

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