Evaluate
-\frac{1}{3t}
Expand
-\frac{1}{3t}
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\frac{\frac{3}{3t}-\frac{t}{3t}}{t-3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t and 3 is 3t. Multiply \frac{1}{t} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{t}{t}.
\frac{\frac{3-t}{3t}}{t-3}
Since \frac{3}{3t} and \frac{t}{3t} have the same denominator, subtract them by subtracting their numerators.
\frac{3-t}{3t\left(t-3\right)}
Express \frac{\frac{3-t}{3t}}{t-3} as a single fraction.
\frac{-\left(t-3\right)}{3t\left(t-3\right)}
Extract the negative sign in 3-t.
\frac{-1}{3t}
Cancel out t-3 in both numerator and denominator.
\frac{\frac{3}{3t}-\frac{t}{3t}}{t-3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t and 3 is 3t. Multiply \frac{1}{t} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{t}{t}.
\frac{\frac{3-t}{3t}}{t-3}
Since \frac{3}{3t} and \frac{t}{3t} have the same denominator, subtract them by subtracting their numerators.
\frac{3-t}{3t\left(t-3\right)}
Express \frac{\frac{3-t}{3t}}{t-3} as a single fraction.
\frac{-\left(t-3\right)}{3t\left(t-3\right)}
Extract the negative sign in 3-t.
\frac{-1}{3t}
Cancel out t-3 in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}