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\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}
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\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}
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\frac{\left(2x-3\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}-\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+2 and x+3 is \left(x+2\right)\left(x+3\right). Multiply \frac{2x-3}{x+2} times \frac{x+3}{x+3}. Multiply \frac{x}{x+3} times \frac{x+2}{x+2}.
\frac{\left(2x-3\right)\left(x+3\right)-x\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
Since \frac{\left(2x-3\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)} and \frac{x\left(x+2\right)}{\left(x+2\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}+6x-3x-9-x^{2}-2x}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
Do the multiplications in \left(2x-3\right)\left(x+3\right)-x\left(x+2\right).
\frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
Combine like terms in 2x^{2}+6x-3x-9-x^{2}-2x.
\frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)}+\frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x+3\right) and x is x\left(x+2\right)\left(x+3\right). Multiply \frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}.
\frac{\left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}
Since \frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)} and \frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{x^{3}+x^{2}-9x+x^{2}+3x+2x+6}{x\left(x+2\right)\left(x+3\right)}
Do the multiplications in \left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right).
\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}
Combine like terms in x^{3}+x^{2}-9x+x^{2}+3x+2x+6.
\frac{x^{3}+2x^{2}-4x+6}{x^{3}+5x^{2}+6x}
Expand x\left(x+2\right)\left(x+3\right).
\frac{\left(2x-3\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}-\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+2 and x+3 is \left(x+2\right)\left(x+3\right). Multiply \frac{2x-3}{x+2} times \frac{x+3}{x+3}. Multiply \frac{x}{x+3} times \frac{x+2}{x+2}.
\frac{\left(2x-3\right)\left(x+3\right)-x\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
Since \frac{\left(2x-3\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)} and \frac{x\left(x+2\right)}{\left(x+2\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}+6x-3x-9-x^{2}-2x}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
Do the multiplications in \left(2x-3\right)\left(x+3\right)-x\left(x+2\right).
\frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}
Combine like terms in 2x^{2}+6x-3x-9-x^{2}-2x.
\frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)}+\frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x+3\right) and x is x\left(x+2\right)\left(x+3\right). Multiply \frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}.
\frac{\left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}
Since \frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)} and \frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{x^{3}+x^{2}-9x+x^{2}+3x+2x+6}{x\left(x+2\right)\left(x+3\right)}
Do the multiplications in \left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right).
\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}
Combine like terms in x^{3}+x^{2}-9x+x^{2}+3x+2x+6.
\frac{x^{3}+2x^{2}-4x+6}{x^{3}+5x^{2}+6x}
Expand x\left(x+2\right)\left(x+3\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
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}