Evaluate
\frac{6\left(x+2\right)}{x\left(x-2\right)\left(x+3\right)}
Expand
\frac{6\left(x+2\right)}{x\left(x^{2}+x-6\right)}
Graph
Share
Copied to clipboard
\frac{-2}{x}+\frac{2x+8}{\left(x-2\right)\left(x+3\right)}
Factor x^{2}+x-6.
\frac{-2\left(x-2\right)\left(x+3\right)}{x\left(x-2\right)\left(x+3\right)}+\frac{\left(2x+8\right)x}{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 x and \left(x-2\right)\left(x+3\right) is x\left(x-2\right)\left(x+3\right). Multiply \frac{-2}{x} times \frac{\left(x-2\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}. Multiply \frac{2x+8}{\left(x-2\right)\left(x+3\right)} times \frac{x}{x}.
\frac{-2\left(x-2\right)\left(x+3\right)+\left(2x+8\right)x}{x\left(x-2\right)\left(x+3\right)}
Since \frac{-2\left(x-2\right)\left(x+3\right)}{x\left(x-2\right)\left(x+3\right)} and \frac{\left(2x+8\right)x}{x\left(x-2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{-2x^{2}-6x+4x+12+2x^{2}+8x}{x\left(x-2\right)\left(x+3\right)}
Do the multiplications in -2\left(x-2\right)\left(x+3\right)+\left(2x+8\right)x.
\frac{6x+12}{x\left(x-2\right)\left(x+3\right)}
Combine like terms in -2x^{2}-6x+4x+12+2x^{2}+8x.
\frac{6x+12}{x^{3}+x^{2}-6x}
Expand x\left(x-2\right)\left(x+3\right).
\frac{-2}{x}+\frac{2x+8}{\left(x-2\right)\left(x+3\right)}
Factor x^{2}+x-6.
\frac{-2\left(x-2\right)\left(x+3\right)}{x\left(x-2\right)\left(x+3\right)}+\frac{\left(2x+8\right)x}{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 x and \left(x-2\right)\left(x+3\right) is x\left(x-2\right)\left(x+3\right). Multiply \frac{-2}{x} times \frac{\left(x-2\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}. Multiply \frac{2x+8}{\left(x-2\right)\left(x+3\right)} times \frac{x}{x}.
\frac{-2\left(x-2\right)\left(x+3\right)+\left(2x+8\right)x}{x\left(x-2\right)\left(x+3\right)}
Since \frac{-2\left(x-2\right)\left(x+3\right)}{x\left(x-2\right)\left(x+3\right)} and \frac{\left(2x+8\right)x}{x\left(x-2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{-2x^{2}-6x+4x+12+2x^{2}+8x}{x\left(x-2\right)\left(x+3\right)}
Do the multiplications in -2\left(x-2\right)\left(x+3\right)+\left(2x+8\right)x.
\frac{6x+12}{x\left(x-2\right)\left(x+3\right)}
Combine like terms in -2x^{2}-6x+4x+12+2x^{2}+8x.
\frac{6x+12}{x^{3}+x^{2}-6x}
Expand x\left(x-2\right)\left(x+3\right).
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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}