Final Answer
Step-by-step Solution
Specify the solving method
The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors
Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete
Simplify the numerators
Combine and simplify all terms in the same fraction with common denominator $\left(x+h\right)h$
Divide fractions $\frac{\frac{-x}{\left(x+h\right)h}}{x}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$
Simplify the fraction $\frac{-x}{\left(x+h\right)hx}$ by $x$
Evaluate the limit $\lim_{x\to0}\left(\frac{-1}{\left(x+h\right)h}\right)$ by replacing all occurrences of $x$ by $0$
$x+0=x$, where $x$ is any expression
When multiplying two powers that have the same base ($h$), you can add the exponents