Answer
$\dfrac{1}{12}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
3^{-1}-4^{-1}
.$ Then change the resulting fractions to similar fractions.
$\bf{\text{Solution Details:}}$
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{3^1}-\dfrac{1}{4^1}
\\\\=
\dfrac{1}{3}-\dfrac{1}{4}
.\end{array}
To subtract the expression above, make the fractions similar (same denominator) by multiplying each term by an expression equal to $1$. The expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{3}\cdot\dfrac{4}{4}-\dfrac{1}{4}\cdot\dfrac{3}{3}
\\\\=
\dfrac{4}{12}-\dfrac{3}{12}
\\\\=
\dfrac{4-3}{12}
\\\\=
\dfrac{1}{12}
.\end{array}
