Take out the constants.
\[\frac{3x-1}{{x}^{2}}+\frac{3}{6}\times \frac{x}{{x}^{2}}\]
Simplify \(\frac{3}{6}\) to \(\frac{1}{2}\).
\[\frac{3x-1}{{x}^{2}}+\frac{1}{2}\times \frac{x}{{x}^{2}}\]
Simplify \(\frac{1}{2}\times \frac{x}{{x}^{2}}\) to \(\frac{x}{2{x}^{2}}\).
\[\frac{3x-1}{{x}^{2}}+\frac{x}{2{x}^{2}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\frac{3x-1}{{x}^{2}}+\frac{{x}^{1-2}}{2}\]
Simplify \(1-2\) to \(-1\).
\[\frac{3x-1}{{x}^{2}}+\frac{{x}^{-1}}{2}\]
Rewrite the expression with a common denominator.
\[\frac{(3x-1)\times 2+{x}^{-1}{x}^{2}}{{x}^{2}\times 2}\]
Regroup terms.
\[\frac{2(3x-1)+{x}^{-1}{x}^{2}}{{x}^{2}\times 2}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{2(3x-1)+{x}^{-1+2}}{{x}^{2}\times 2}\]
Simplify \(-1+2\) to \(1\).
\[\frac{2(3x-1)+{x}^{1}}{{x}^{2}\times 2}\]
Use Rule of One: \({x}^{1}=x\).
\[\frac{2(3x-1)+x}{{x}^{2}\times 2}\]
Expand.
\[\frac{6x-2+x}{{x}^{2}\times 2}\]
Collect like terms.
\[\frac{(6x+x)-2}{{x}^{2}\times 2}\]
Simplify \((6x+x)-2\) to \(7x-2\).
\[\frac{7x-2}{{x}^{2}\times 2}\]
Regroup terms.
\[\frac{7x-2}{2{x}^{2}}\]
(7*x-2)/(2*x^2)
