Evaluate
\frac{2\left(31x^{2}+2x+15\right)}{\left(x-3\right)\left(3x+1\right)}
Expand
\frac{2\left(31x^{2}+2x+15\right)}{\left(x-3\right)\left(3x+1\right)}
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\frac{\left(8x+36\right)\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)}+\frac{\left(38x+2\right)\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x+1 is \left(x-3\right)\left(3x+1\right). Multiply \frac{8x+36}{x-3} times \frac{3x+1}{3x+1}. Multiply \frac{38x+2}{3x+1} times \frac{x-3}{x-3}.
\frac{\left(8x+36\right)\left(3x+1\right)+\left(38x+2\right)\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}
Since \frac{\left(8x+36\right)\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)} and \frac{\left(38x+2\right)\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)} have the same denominator, add them by adding their numerators.
\frac{24x^{2}+8x+108x+36+38x^{2}-114x+2x-6}{\left(x-3\right)\left(3x+1\right)}
Do the multiplications in \left(8x+36\right)\left(3x+1\right)+\left(38x+2\right)\left(x-3\right).
\frac{62x^{2}+4x+30}{\left(x-3\right)\left(3x+1\right)}
Combine like terms in 24x^{2}+8x+108x+36+38x^{2}-114x+2x-6.
\frac{62x^{2}+4x+30}{3x^{2}-8x-3}
Expand \left(x-3\right)\left(3x+1\right).
\frac{\left(8x+36\right)\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)}+\frac{\left(38x+2\right)\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x+1 is \left(x-3\right)\left(3x+1\right). Multiply \frac{8x+36}{x-3} times \frac{3x+1}{3x+1}. Multiply \frac{38x+2}{3x+1} times \frac{x-3}{x-3}.
\frac{\left(8x+36\right)\left(3x+1\right)+\left(38x+2\right)\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}
Since \frac{\left(8x+36\right)\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)} and \frac{\left(38x+2\right)\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)} have the same denominator, add them by adding their numerators.
\frac{24x^{2}+8x+108x+36+38x^{2}-114x+2x-6}{\left(x-3\right)\left(3x+1\right)}
Do the multiplications in \left(8x+36\right)\left(3x+1\right)+\left(38x+2\right)\left(x-3\right).
\frac{62x^{2}+4x+30}{\left(x-3\right)\left(3x+1\right)}
Combine like terms in 24x^{2}+8x+108x+36+38x^{2}-114x+2x-6.
\frac{62x^{2}+4x+30}{3x^{2}-8x-3}
Expand \left(x-3\right)\left(3x+1\right).
Examples
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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
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