Evaluate
\frac{3-x}{2\left(x+3\right)}
Expand
-\frac{x-3}{2\left(x+3\right)}
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\frac{1}{x-3}+\frac{1-x}{2\left(x+3\right)}-\frac{6}{x^{2}-9}
Factor 6+2x.
\frac{2\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)}+\frac{\left(1-x\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 2\left(x+3\right) is 2\left(x-3\right)\left(x+3\right). Multiply \frac{1}{x-3} times \frac{2\left(x+3\right)}{2\left(x+3\right)}. Multiply \frac{1-x}{2\left(x+3\right)} times \frac{x-3}{x-3}.
\frac{2\left(x+3\right)+\left(1-x\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
Since \frac{2\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)} and \frac{\left(1-x\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{2x+6+x-3-x^{2}+3x}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
Do the multiplications in 2\left(x+3\right)+\left(1-x\right)\left(x-3\right).
\frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
Combine like terms in 2x+6+x-3-x^{2}+3x.
\frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}-9.
\frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)}-\frac{6\times 2}{2\left(x-3\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-3\right)\left(x+3\right) and \left(x-3\right)\left(x+3\right) is 2\left(x-3\right)\left(x+3\right). Multiply \frac{6}{\left(x-3\right)\left(x+3\right)} times \frac{2}{2}.
\frac{6x+3-x^{2}-6\times 2}{2\left(x-3\right)\left(x+3\right)}
Since \frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)} and \frac{6\times 2}{2\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x+3-x^{2}-12}{2\left(x-3\right)\left(x+3\right)}
Do the multiplications in 6x+3-x^{2}-6\times 2.
\frac{6x-9-x^{2}}{2\left(x-3\right)\left(x+3\right)}
Combine like terms in 6x+3-x^{2}-12.
\frac{\left(x-3\right)\left(-x+3\right)}{2\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{6x-9-x^{2}}{2\left(x-3\right)\left(x+3\right)}.
\frac{-\left(x-3\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}
Extract the negative sign in 3-x.
\frac{-\left(x-3\right)}{2\left(x+3\right)}
Cancel out x-3 in both numerator and denominator.
\frac{-\left(x-3\right)}{2x+6}
Expand 2\left(x+3\right).
\frac{-x+3}{2x+6}
To find the opposite of x-3, find the opposite of each term.
\frac{1}{x-3}+\frac{1-x}{2\left(x+3\right)}-\frac{6}{x^{2}-9}
Factor 6+2x.
\frac{2\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)}+\frac{\left(1-x\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 2\left(x+3\right) is 2\left(x-3\right)\left(x+3\right). Multiply \frac{1}{x-3} times \frac{2\left(x+3\right)}{2\left(x+3\right)}. Multiply \frac{1-x}{2\left(x+3\right)} times \frac{x-3}{x-3}.
\frac{2\left(x+3\right)+\left(1-x\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
Since \frac{2\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)} and \frac{\left(1-x\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{2x+6+x-3-x^{2}+3x}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
Do the multiplications in 2\left(x+3\right)+\left(1-x\right)\left(x-3\right).
\frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{x^{2}-9}
Combine like terms in 2x+6+x-3-x^{2}+3x.
\frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)}-\frac{6}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}-9.
\frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)}-\frac{6\times 2}{2\left(x-3\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-3\right)\left(x+3\right) and \left(x-3\right)\left(x+3\right) is 2\left(x-3\right)\left(x+3\right). Multiply \frac{6}{\left(x-3\right)\left(x+3\right)} times \frac{2}{2}.
\frac{6x+3-x^{2}-6\times 2}{2\left(x-3\right)\left(x+3\right)}
Since \frac{6x+3-x^{2}}{2\left(x-3\right)\left(x+3\right)} and \frac{6\times 2}{2\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x+3-x^{2}-12}{2\left(x-3\right)\left(x+3\right)}
Do the multiplications in 6x+3-x^{2}-6\times 2.
\frac{6x-9-x^{2}}{2\left(x-3\right)\left(x+3\right)}
Combine like terms in 6x+3-x^{2}-12.
\frac{\left(x-3\right)\left(-x+3\right)}{2\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{6x-9-x^{2}}{2\left(x-3\right)\left(x+3\right)}.
\frac{-\left(x-3\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}
Extract the negative sign in 3-x.
\frac{-\left(x-3\right)}{2\left(x+3\right)}
Cancel out x-3 in both numerator and denominator.
\frac{-\left(x-3\right)}{2x+6}
Expand 2\left(x+3\right).
\frac{-x+3}{2x+6}
To find the opposite of x-3, find the opposite of each term.
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}