Evaluate
\frac{33+7x-x^{2}}{\left(x+3\right)\left(x+6\right)}
Expand
\frac{33+7x-x^{2}}{\left(x+3\right)\left(x+6\right)}
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\frac{x+6}{\left(x+3\right)\left(x+6\right)}-\frac{\left(x-9\right)\left(x+3\right)}{\left(x+3\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x+6 is \left(x+3\right)\left(x+6\right). Multiply \frac{1}{x+3} times \frac{x+6}{x+6}. Multiply \frac{x-9}{x+6} times \frac{x+3}{x+3}.
\frac{x+6-\left(x-9\right)\left(x+3\right)}{\left(x+3\right)\left(x+6\right)}
Since \frac{x+6}{\left(x+3\right)\left(x+6\right)} and \frac{\left(x-9\right)\left(x+3\right)}{\left(x+3\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+6-x^{2}-3x+9x+27}{\left(x+3\right)\left(x+6\right)}
Do the multiplications in x+6-\left(x-9\right)\left(x+3\right).
\frac{7x+33-x^{2}}{\left(x+3\right)\left(x+6\right)}
Combine like terms in x+6-x^{2}-3x+9x+27.
\frac{7x+33-x^{2}}{x^{2}+9x+18}
Expand \left(x+3\right)\left(x+6\right).
\frac{x+6}{\left(x+3\right)\left(x+6\right)}-\frac{\left(x-9\right)\left(x+3\right)}{\left(x+3\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x+6 is \left(x+3\right)\left(x+6\right). Multiply \frac{1}{x+3} times \frac{x+6}{x+6}. Multiply \frac{x-9}{x+6} times \frac{x+3}{x+3}.
\frac{x+6-\left(x-9\right)\left(x+3\right)}{\left(x+3\right)\left(x+6\right)}
Since \frac{x+6}{\left(x+3\right)\left(x+6\right)} and \frac{\left(x-9\right)\left(x+3\right)}{\left(x+3\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+6-x^{2}-3x+9x+27}{\left(x+3\right)\left(x+6\right)}
Do the multiplications in x+6-\left(x-9\right)\left(x+3\right).
\frac{7x+33-x^{2}}{\left(x+3\right)\left(x+6\right)}
Combine like terms in x+6-x^{2}-3x+9x+27.
\frac{7x+33-x^{2}}{x^{2}+9x+18}
Expand \left(x+3\right)\left(x+6\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}