Evaluate
\frac{2\left(a-17\right)}{3\left(2-a\right)}
Expand
-\frac{2\left(a-17\right)}{3\left(a-2\right)}
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\frac{22}{2a-4}+\frac{2a-1}{6-3a}
Add 21 and 1 to get 22.
\frac{22}{2\left(a-2\right)}+\frac{2a-1}{3\left(-a+2\right)}
Factor 2a-4. Factor 6-3a.
\frac{22\times 3}{6\left(a-2\right)}+\frac{-2\left(2a-1\right)}{6\left(a-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(a-2\right) and 3\left(-a+2\right) is 6\left(a-2\right). Multiply \frac{22}{2\left(a-2\right)} times \frac{3}{3}. Multiply \frac{2a-1}{3\left(-a+2\right)} times \frac{-2}{-2}.
\frac{22\times 3-2\left(2a-1\right)}{6\left(a-2\right)}
Since \frac{22\times 3}{6\left(a-2\right)} and \frac{-2\left(2a-1\right)}{6\left(a-2\right)} have the same denominator, add them by adding their numerators.
\frac{66-4a+2}{6\left(a-2\right)}
Do the multiplications in 22\times 3-2\left(2a-1\right).
\frac{68-4a}{6\left(a-2\right)}
Combine like terms in 66-4a+2.
\frac{4\left(-a+17\right)}{6\left(a-2\right)}
Factor the expressions that are not already factored in \frac{68-4a}{6\left(a-2\right)}.
\frac{2\left(-a+17\right)}{3\left(a-2\right)}
Cancel out 2 in both numerator and denominator.
\frac{2\left(-a+17\right)}{3a-6}
Expand 3\left(a-2\right).
\frac{-2a+34}{3a-6}
Use the distributive property to multiply 2 by -a+17.
\frac{22}{2a-4}+\frac{2a-1}{6-3a}
Add 21 and 1 to get 22.
\frac{22}{2\left(a-2\right)}+\frac{2a-1}{3\left(-a+2\right)}
Factor 2a-4. Factor 6-3a.
\frac{22\times 3}{6\left(a-2\right)}+\frac{-2\left(2a-1\right)}{6\left(a-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(a-2\right) and 3\left(-a+2\right) is 6\left(a-2\right). Multiply \frac{22}{2\left(a-2\right)} times \frac{3}{3}. Multiply \frac{2a-1}{3\left(-a+2\right)} times \frac{-2}{-2}.
\frac{22\times 3-2\left(2a-1\right)}{6\left(a-2\right)}
Since \frac{22\times 3}{6\left(a-2\right)} and \frac{-2\left(2a-1\right)}{6\left(a-2\right)} have the same denominator, add them by adding their numerators.
\frac{66-4a+2}{6\left(a-2\right)}
Do the multiplications in 22\times 3-2\left(2a-1\right).
\frac{68-4a}{6\left(a-2\right)}
Combine like terms in 66-4a+2.
\frac{4\left(-a+17\right)}{6\left(a-2\right)}
Factor the expressions that are not already factored in \frac{68-4a}{6\left(a-2\right)}.
\frac{2\left(-a+17\right)}{3\left(a-2\right)}
Cancel out 2 in both numerator and denominator.
\frac{2\left(-a+17\right)}{3a-6}
Expand 3\left(a-2\right).
\frac{-2a+34}{3a-6}
Use the distributive property to multiply 2 by -a+17.
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}