Evaluate
4\left(x^{2}-6\right)
Expand
4x^{2}-24
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\left(\frac{\left(x+3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{x+3}{x-3} times \frac{x+3}{x+3}. Multiply \frac{x-3}{x+3} times \frac{x-3}{x-3}.
\left(\frac{\left(x+3\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
Since \frac{\left(x+3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\left(\frac{x^{2}+3x+3x+9-x^{2}+3x+3x-9}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
Do the multiplications in \left(x+3\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right).
\left(\frac{12x}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
Combine like terms in x^{2}+3x+3x+9-x^{2}+3x+3x-9.
\left(\frac{12x}{\left(x-3\right)\left(x+3\right)}+\frac{4x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\right)\left(x-\frac{9}{x}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.
\frac{12x+4x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\left(x-\frac{9}{x}\right)
Since \frac{12x}{\left(x-3\right)\left(x+3\right)} and \frac{4x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{12x+4x^{3}+12x^{2}-12x^{2}-36x}{\left(x-3\right)\left(x+3\right)}\left(x-\frac{9}{x}\right)
Do the multiplications in 12x+4x\left(x-3\right)\left(x+3\right).
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\left(x-\frac{9}{x}\right)
Combine like terms in 12x+4x^{3}+12x^{2}-12x^{2}-36x.
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\left(\frac{xx}{x}-\frac{9}{x}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\times \frac{xx-9}{x}
Since \frac{xx}{x} and \frac{9}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\times \frac{x^{2}-9}{x}
Do the multiplications in xx-9.
\frac{\left(-24x+4x^{3}\right)\left(x^{2}-9\right)}{\left(x-3\right)\left(x+3\right)x}
Multiply \frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)} times \frac{x^{2}-9}{x} by multiplying numerator times numerator and denominator times denominator.
\frac{4x\left(x-3\right)\left(x+3\right)\left(x^{2}-6\right)}{x\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
4\left(x^{2}-6\right)
Cancel out x\left(x-3\right)\left(x+3\right) in both numerator and denominator.
4x^{2}-24
Expand the expression.
\left(\frac{\left(x+3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{x+3}{x-3} times \frac{x+3}{x+3}. Multiply \frac{x-3}{x+3} times \frac{x-3}{x-3}.
\left(\frac{\left(x+3\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
Since \frac{\left(x+3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\left(\frac{x^{2}+3x+3x+9-x^{2}+3x+3x-9}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
Do the multiplications in \left(x+3\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right).
\left(\frac{12x}{\left(x-3\right)\left(x+3\right)}+4x\right)\left(x-\frac{9}{x}\right)
Combine like terms in x^{2}+3x+3x+9-x^{2}+3x+3x-9.
\left(\frac{12x}{\left(x-3\right)\left(x+3\right)}+\frac{4x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\right)\left(x-\frac{9}{x}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.
\frac{12x+4x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\left(x-\frac{9}{x}\right)
Since \frac{12x}{\left(x-3\right)\left(x+3\right)} and \frac{4x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{12x+4x^{3}+12x^{2}-12x^{2}-36x}{\left(x-3\right)\left(x+3\right)}\left(x-\frac{9}{x}\right)
Do the multiplications in 12x+4x\left(x-3\right)\left(x+3\right).
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\left(x-\frac{9}{x}\right)
Combine like terms in 12x+4x^{3}+12x^{2}-12x^{2}-36x.
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\left(\frac{xx}{x}-\frac{9}{x}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\times \frac{xx-9}{x}
Since \frac{xx}{x} and \frac{9}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)}\times \frac{x^{2}-9}{x}
Do the multiplications in xx-9.
\frac{\left(-24x+4x^{3}\right)\left(x^{2}-9\right)}{\left(x-3\right)\left(x+3\right)x}
Multiply \frac{-24x+4x^{3}}{\left(x-3\right)\left(x+3\right)} times \frac{x^{2}-9}{x} by multiplying numerator times numerator and denominator times denominator.
\frac{4x\left(x-3\right)\left(x+3\right)\left(x^{2}-6\right)}{x\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
4\left(x^{2}-6\right)
Cancel out x\left(x-3\right)\left(x+3\right) in both numerator and denominator.
4x^{2}-24
Expand the expression.
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}