Answer
$\lim_{x\to1}\dfrac{f(x)g(x)}{h(x)}=12$
Work Step by Step
$\lim_{x\to1}\dfrac{f(x)g(x)}{h(x)}$
It is known that $\lim_{x\to1}f(x)=8$ $,$ $\lim_{x\to1}g(x)=3$ and $\lim_{x\to1}h(x)=2$
Evaluate the limit using the limit laws:
$\lim_{x\to1}\dfrac{f(x)g(x)}{h(x)}=...$
If the limit of the denominator is different from $0$, then the limit of a quotient is the quotient of the limits of the numerator and the denominator:
$...=\dfrac{\lim_{x\to1}f(x)g(x)}{\lim_{x\to1}h(x)}=...$
The limit of a product is the product of the limits of the factors:
$...=\dfrac{[\lim_{x\to1}f(x)][\lim_{x\to1}g(x)]}{\lim_{x\to1}h(x)}=...$
The limits indicated are known. Substitute them into the expression and evaluate:
$...=\dfrac{(8)(3)}{2}=(4)(3)=12$
