Evaluate
\frac{9+13x-2x^{2}}{x\left(x+3\right)}
Expand
\frac{9+13x-2x^{2}}{x\left(x+3\right)}
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\frac{\left(5x+3\right)\left(x+3\right)}{x\left(x+3\right)}-\frac{\left(7x+5\right)x}{x\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x+3 is x\left(x+3\right). Multiply \frac{5x+3}{x} times \frac{x+3}{x+3}. Multiply \frac{7x+5}{x+3} times \frac{x}{x}.
\frac{\left(5x+3\right)\left(x+3\right)-\left(7x+5\right)x}{x\left(x+3\right)}
Since \frac{\left(5x+3\right)\left(x+3\right)}{x\left(x+3\right)} and \frac{\left(7x+5\right)x}{x\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x^{2}+15x+3x+9-7x^{2}-5x}{x\left(x+3\right)}
Do the multiplications in \left(5x+3\right)\left(x+3\right)-\left(7x+5\right)x.
\frac{-2x^{2}+13x+9}{x\left(x+3\right)}
Combine like terms in 5x^{2}+15x+3x+9-7x^{2}-5x.
\frac{-2x^{2}+13x+9}{x^{2}+3x}
Expand x\left(x+3\right).
\frac{\left(5x+3\right)\left(x+3\right)}{x\left(x+3\right)}-\frac{\left(7x+5\right)x}{x\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x+3 is x\left(x+3\right). Multiply \frac{5x+3}{x} times \frac{x+3}{x+3}. Multiply \frac{7x+5}{x+3} times \frac{x}{x}.
\frac{\left(5x+3\right)\left(x+3\right)-\left(7x+5\right)x}{x\left(x+3\right)}
Since \frac{\left(5x+3\right)\left(x+3\right)}{x\left(x+3\right)} and \frac{\left(7x+5\right)x}{x\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x^{2}+15x+3x+9-7x^{2}-5x}{x\left(x+3\right)}
Do the multiplications in \left(5x+3\right)\left(x+3\right)-\left(7x+5\right)x.
\frac{-2x^{2}+13x+9}{x\left(x+3\right)}
Combine like terms in 5x^{2}+15x+3x+9-7x^{2}-5x.
\frac{-2x^{2}+13x+9}{x^{2}+3x}
Expand x\left(x+3\right).
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y = 3x + 4
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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}