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\frac{3}{X}
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\frac{3}{X}
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\frac{\frac{XX}{X\left(X-3\right)}+\frac{\left(X-3\right)\left(X-3\right)}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of X-3 and X is X\left(X-3\right). Multiply \frac{X}{X-3} times \frac{X}{X}. Multiply \frac{X-3}{X} times \frac{X-3}{X-3}.
\frac{\frac{XX+\left(X-3\right)\left(X-3\right)}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Since \frac{XX}{X\left(X-3\right)} and \frac{\left(X-3\right)\left(X-3\right)}{X\left(X-3\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{X^{2}+X^{2}-3X-3X+9}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Do the multiplications in XX+\left(X-3\right)\left(X-3\right).
\frac{\frac{2X^{2}-6X+9}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Combine like terms in X^{2}+X^{2}-3X-3X+9.
\frac{\frac{2X^{2}-6X+9}{X\left(X-3\right)}-\frac{X\left(X-3\right)}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{X\left(X-3\right)}{X\left(X-3\right)}.
\frac{\frac{2X^{2}-6X+9-X\left(X-3\right)}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Since \frac{2X^{2}-6X+9}{X\left(X-3\right)} and \frac{X\left(X-3\right)}{X\left(X-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{2X^{2}-6X+9-X^{2}+3X}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Do the multiplications in 2X^{2}-6X+9-X\left(X-3\right).
\frac{\frac{X^{2}-3X+9}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Combine like terms in 2X^{2}-6X+9-X^{2}+3X.
\frac{\left(X^{2}-3X+9\right)\times 3\left(X-3\right)}{X\left(X-3\right)\left(X^{2}-3X+9\right)}
Divide \frac{X^{2}-3X+9}{X\left(X-3\right)} by \frac{X^{2}-3X+9}{3\left(X-3\right)} by multiplying \frac{X^{2}-3X+9}{X\left(X-3\right)} by the reciprocal of \frac{X^{2}-3X+9}{3\left(X-3\right)}.
\frac{3}{X}
Cancel out \left(X-3\right)\left(X^{2}-3X+9\right) in both numerator and denominator.
\frac{\frac{XX}{X\left(X-3\right)}+\frac{\left(X-3\right)\left(X-3\right)}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of X-3 and X is X\left(X-3\right). Multiply \frac{X}{X-3} times \frac{X}{X}. Multiply \frac{X-3}{X} times \frac{X-3}{X-3}.
\frac{\frac{XX+\left(X-3\right)\left(X-3\right)}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Since \frac{XX}{X\left(X-3\right)} and \frac{\left(X-3\right)\left(X-3\right)}{X\left(X-3\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{X^{2}+X^{2}-3X-3X+9}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Do the multiplications in XX+\left(X-3\right)\left(X-3\right).
\frac{\frac{2X^{2}-6X+9}{X\left(X-3\right)}-1}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Combine like terms in X^{2}+X^{2}-3X-3X+9.
\frac{\frac{2X^{2}-6X+9}{X\left(X-3\right)}-\frac{X\left(X-3\right)}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{X\left(X-3\right)}{X\left(X-3\right)}.
\frac{\frac{2X^{2}-6X+9-X\left(X-3\right)}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Since \frac{2X^{2}-6X+9}{X\left(X-3\right)} and \frac{X\left(X-3\right)}{X\left(X-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{2X^{2}-6X+9-X^{2}+3X}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Do the multiplications in 2X^{2}-6X+9-X\left(X-3\right).
\frac{\frac{X^{2}-3X+9}{X\left(X-3\right)}}{\frac{X^{2}-3X+9}{3\left(X-3\right)}}
Combine like terms in 2X^{2}-6X+9-X^{2}+3X.
\frac{\left(X^{2}-3X+9\right)\times 3\left(X-3\right)}{X\left(X-3\right)\left(X^{2}-3X+9\right)}
Divide \frac{X^{2}-3X+9}{X\left(X-3\right)} by \frac{X^{2}-3X+9}{3\left(X-3\right)} by multiplying \frac{X^{2}-3X+9}{X\left(X-3\right)} by the reciprocal of \frac{X^{2}-3X+9}{3\left(X-3\right)}.
\frac{3}{X}
Cancel out \left(X-3\right)\left(X^{2}-3X+9\right) in both numerator and denominator.
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}