Evaluate
\frac{8-x}{3\left(x^{2}-9\right)}
Expand
-\frac{x-8}{3\left(x^{2}-9\right)}
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\frac{3}{3\left(x-3\right)}-\frac{1}{x+3}-\frac{x+10}{3x^{2}-27}
Factor 3x-9.
\frac{3\left(x+3\right)}{3\left(x-3\right)\left(x+3\right)}-\frac{3\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-3\right) and x+3 is 3\left(x-3\right)\left(x+3\right). Multiply \frac{3}{3\left(x-3\right)} times \frac{x+3}{x+3}. Multiply \frac{1}{x+3} times \frac{3\left(x-3\right)}{3\left(x-3\right)}.
\frac{3\left(x+3\right)-3\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
Since \frac{3\left(x+3\right)}{3\left(x-3\right)\left(x+3\right)} and \frac{3\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+9-3x+9}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
Do the multiplications in 3\left(x+3\right)-3\left(x-3\right).
\frac{18}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
Combine like terms in 3x+9-3x+9.
\frac{18}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3\left(x-3\right)\left(x+3\right)}
Factor 3x^{2}-27.
\frac{18-\left(x+10\right)}{3\left(x-3\right)\left(x+3\right)}
Since \frac{18}{3\left(x-3\right)\left(x+3\right)} and \frac{x+10}{3\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{18-x-10}{3\left(x-3\right)\left(x+3\right)}
Do the multiplications in 18-\left(x+10\right).
\frac{8-x}{3\left(x-3\right)\left(x+3\right)}
Combine like terms in 18-x-10.
\frac{8-x}{3x^{2}-27}
Expand 3\left(x-3\right)\left(x+3\right).
\frac{3}{3\left(x-3\right)}-\frac{1}{x+3}-\frac{x+10}{3x^{2}-27}
Factor 3x-9.
\frac{3\left(x+3\right)}{3\left(x-3\right)\left(x+3\right)}-\frac{3\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-3\right) and x+3 is 3\left(x-3\right)\left(x+3\right). Multiply \frac{3}{3\left(x-3\right)} times \frac{x+3}{x+3}. Multiply \frac{1}{x+3} times \frac{3\left(x-3\right)}{3\left(x-3\right)}.
\frac{3\left(x+3\right)-3\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
Since \frac{3\left(x+3\right)}{3\left(x-3\right)\left(x+3\right)} and \frac{3\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+9-3x+9}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
Do the multiplications in 3\left(x+3\right)-3\left(x-3\right).
\frac{18}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3x^{2}-27}
Combine like terms in 3x+9-3x+9.
\frac{18}{3\left(x-3\right)\left(x+3\right)}-\frac{x+10}{3\left(x-3\right)\left(x+3\right)}
Factor 3x^{2}-27.
\frac{18-\left(x+10\right)}{3\left(x-3\right)\left(x+3\right)}
Since \frac{18}{3\left(x-3\right)\left(x+3\right)} and \frac{x+10}{3\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{18-x-10}{3\left(x-3\right)\left(x+3\right)}
Do the multiplications in 18-\left(x+10\right).
\frac{8-x}{3\left(x-3\right)\left(x+3\right)}
Combine like terms in 18-x-10.
\frac{8-x}{3x^{2}-27}
Expand 3\left(x-3\right)\left(x+3\right).
Examples
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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
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