Evaluate
\frac{2x^{2}+13x-21}{x-1}
Expand
\frac{2x^{2}+13x-21}{x-1}
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11+x+\frac{x^{2}+3x-10}{x-1}
Add 6 and 5 to get 11.
\frac{\left(11+x\right)\left(x-1\right)}{x-1}+\frac{x^{2}+3x-10}{x-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 11+x times \frac{x-1}{x-1}.
\frac{\left(11+x\right)\left(x-1\right)+x^{2}+3x-10}{x-1}
Since \frac{\left(11+x\right)\left(x-1\right)}{x-1} and \frac{x^{2}+3x-10}{x-1} have the same denominator, add them by adding their numerators.
\frac{11x-11+x^{2}-x+x^{2}+3x-10}{x-1}
Do the multiplications in \left(11+x\right)\left(x-1\right)+x^{2}+3x-10.
\frac{13x-21+2x^{2}}{x-1}
Combine like terms in 11x-11+x^{2}-x+x^{2}+3x-10.
11+x+\frac{x^{2}+3x-10}{x-1}
Add 6 and 5 to get 11.
\frac{\left(11+x\right)\left(x-1\right)}{x-1}+\frac{x^{2}+3x-10}{x-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 11+x times \frac{x-1}{x-1}.
\frac{\left(11+x\right)\left(x-1\right)+x^{2}+3x-10}{x-1}
Since \frac{\left(11+x\right)\left(x-1\right)}{x-1} and \frac{x^{2}+3x-10}{x-1} have the same denominator, add them by adding their numerators.
\frac{11x-11+x^{2}-x+x^{2}+3x-10}{x-1}
Do the multiplications in \left(11+x\right)\left(x-1\right)+x^{2}+3x-10.
\frac{13x-21+2x^{2}}{x-1}
Combine like terms in 11x-11+x^{2}-x+x^{2}+3x-10.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
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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}