Evaluate
\frac{a-6b}{3ab}
Expand
-\frac{6b-a}{3ab}
Share
Copied to clipboard
\frac{\left(a-4\right)\times 3b}{6ab}-\frac{\left(9b-2\right)a}{6ab}+1
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 6b is 6ab. Multiply \frac{a-4}{2a} times \frac{3b}{3b}. Multiply \frac{9b-2}{6b} times \frac{a}{a}.
\frac{\left(a-4\right)\times 3b-\left(9b-2\right)a}{6ab}+1
Since \frac{\left(a-4\right)\times 3b}{6ab} and \frac{\left(9b-2\right)a}{6ab} have the same denominator, subtract them by subtracting their numerators.
\frac{3ab-12b-9ba+2a}{6ab}+1
Do the multiplications in \left(a-4\right)\times 3b-\left(9b-2\right)a.
\frac{-6ab-12b+2a}{6ab}+1
Combine like terms in 3ab-12b-9ba+2a.
\frac{2\left(-3ab+a-6b\right)}{6ab}+1
Factor the expressions that are not already factored in \frac{-6ab-12b+2a}{6ab}.
\frac{-3ab+a-6b}{3ab}+1
Cancel out 2 in both numerator and denominator.
\frac{-3ab+a-6b}{3ab}+\frac{3ab}{3ab}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3ab}{3ab}.
\frac{-3ab+a-6b+3ab}{3ab}
Since \frac{-3ab+a-6b}{3ab} and \frac{3ab}{3ab} have the same denominator, add them by adding their numerators.
\frac{a-6b}{3ab}
Combine like terms in -3ab+a-6b+3ab.
\frac{\left(a-4\right)\times 3b}{6ab}-\frac{\left(9b-2\right)a}{6ab}+1
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 6b is 6ab. Multiply \frac{a-4}{2a} times \frac{3b}{3b}. Multiply \frac{9b-2}{6b} times \frac{a}{a}.
\frac{\left(a-4\right)\times 3b-\left(9b-2\right)a}{6ab}+1
Since \frac{\left(a-4\right)\times 3b}{6ab} and \frac{\left(9b-2\right)a}{6ab} have the same denominator, subtract them by subtracting their numerators.
\frac{3ab-12b-9ba+2a}{6ab}+1
Do the multiplications in \left(a-4\right)\times 3b-\left(9b-2\right)a.
\frac{-6ab-12b+2a}{6ab}+1
Combine like terms in 3ab-12b-9ba+2a.
\frac{2\left(-3ab+a-6b\right)}{6ab}+1
Factor the expressions that are not already factored in \frac{-6ab-12b+2a}{6ab}.
\frac{-3ab+a-6b}{3ab}+1
Cancel out 2 in both numerator and denominator.
\frac{-3ab+a-6b}{3ab}+\frac{3ab}{3ab}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3ab}{3ab}.
\frac{-3ab+a-6b+3ab}{3ab}
Since \frac{-3ab+a-6b}{3ab} and \frac{3ab}{3ab} have the same denominator, add them by adding their numerators.
\frac{a-6b}{3ab}
Combine like terms in -3ab+a-6b+3ab.
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}