Evaluate
\frac{a\left(19-2a\right)}{\left(a-2\right)\left(a+1\right)}
Factor
\frac{a\left(19-2a\right)}{\left(a-2\right)\left(a+1\right)}
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\frac{5a\left(a+1\right)}{\left(a-2\right)\left(a+1\right)}-\frac{7a\left(a-2\right)}{\left(a-2\right)\left(a+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-2 and a+1 is \left(a-2\right)\left(a+1\right). Multiply \frac{5a}{a-2} times \frac{a+1}{a+1}. Multiply \frac{7a}{a+1} times \frac{a-2}{a-2}.
\frac{5a\left(a+1\right)-7a\left(a-2\right)}{\left(a-2\right)\left(a+1\right)}
Since \frac{5a\left(a+1\right)}{\left(a-2\right)\left(a+1\right)} and \frac{7a\left(a-2\right)}{\left(a-2\right)\left(a+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5a^{2}+5a-7a^{2}+14a}{\left(a-2\right)\left(a+1\right)}
Do the multiplications in 5a\left(a+1\right)-7a\left(a-2\right).
\frac{-2a^{2}+19a}{\left(a-2\right)\left(a+1\right)}
Combine like terms in 5a^{2}+5a-7a^{2}+14a.
\frac{-2a^{2}+19a}{a^{2}-a-2}
Expand \left(a-2\right)\left(a+1\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}