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\frac{3x-2}{2\left(x-3\right)}-\frac{3x+2}{3\left(x-3\right)}-\frac{3x-8}{18-6x}
Factor 2x-6. Factor 3x-9.
\frac{3\left(3x-2\right)}{6\left(x-3\right)}-\frac{2\left(3x+2\right)}{6\left(x-3\right)}-\frac{3x-8}{18-6x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-3\right) and 3\left(x-3\right) is 6\left(x-3\right). Multiply \frac{3x-2}{2\left(x-3\right)} times \frac{3}{3}. Multiply \frac{3x+2}{3\left(x-3\right)} times \frac{2}{2}.
\frac{3\left(3x-2\right)-2\left(3x+2\right)}{6\left(x-3\right)}-\frac{3x-8}{18-6x}
Since \frac{3\left(3x-2\right)}{6\left(x-3\right)} and \frac{2\left(3x+2\right)}{6\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9x-6-6x-4}{6\left(x-3\right)}-\frac{3x-8}{18-6x}
Do the multiplications in 3\left(3x-2\right)-2\left(3x+2\right).
\frac{3x-10}{6\left(x-3\right)}-\frac{3x-8}{18-6x}
Combine like terms in 9x-6-6x-4.
\frac{3x-10}{6\left(x-3\right)}-\frac{3x-8}{6\left(-x+3\right)}
Factor 18-6x.
\frac{3x-10}{6\left(x-3\right)}-\frac{-\left(3x-8\right)}{6\left(x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6\left(x-3\right) and 6\left(-x+3\right) is 6\left(x-3\right). Multiply \frac{3x-8}{6\left(-x+3\right)} times \frac{-1}{-1}.
\frac{3x-10-\left(-\left(3x-8\right)\right)}{6\left(x-3\right)}
Since \frac{3x-10}{6\left(x-3\right)} and \frac{-\left(3x-8\right)}{6\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x-10+3x-8}{6\left(x-3\right)}
Do the multiplications in 3x-10-\left(-\left(3x-8\right)\right).
\frac{6x-18}{6\left(x-3\right)}
Combine like terms in 3x-10+3x-8.
\frac{6\left(x-3\right)}{6\left(x-3\right)}
Factor the expressions that are not already factored in \frac{6x-18}{6\left(x-3\right)}.
1
Cancel out 6\left(x-3\right) 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}