Evaluate
-\frac{12}{\left(3a-1\right)\left(3x+3a-1\right)}
Expand
-\frac{12}{\left(3a-1\right)\left(3x+3a-1\right)}
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\frac{\frac{4\left(3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)}-\frac{4\left(3x+3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a+3x-1 and 3a-1 is \left(3a-1\right)\left(3x+3a-1\right). Multiply \frac{4}{3a+3x-1} times \frac{3a-1}{3a-1}. Multiply \frac{4}{3a-1} times \frac{3x+3a-1}{3x+3a-1}.
\frac{\frac{4\left(3a-1\right)-4\left(3x+3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
Since \frac{4\left(3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)} and \frac{4\left(3x+3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{12a-4-12x-12a+4}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
Do the multiplications in 4\left(3a-1\right)-4\left(3x+3a-1\right).
\frac{\frac{-12x}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
Combine like terms in 12a-4-12x-12a+4.
\frac{-12x}{\left(3a-1\right)\left(3x+3a-1\right)x}
Express \frac{\frac{-12x}{\left(3a-1\right)\left(3x+3a-1\right)}}{x} as a single fraction.
\frac{-12}{\left(3a-1\right)\left(3x+3a-1\right)}
Cancel out x in both numerator and denominator.
\frac{-12}{9ax+9a^{2}-3a-3x-3a+1}
Apply the distributive property by multiplying each term of 3a-1 by each term of 3x+3a-1.
\frac{-12}{9ax+9a^{2}-6a-3x+1}
Combine -3a and -3a to get -6a.
\frac{\frac{4\left(3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)}-\frac{4\left(3x+3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a+3x-1 and 3a-1 is \left(3a-1\right)\left(3x+3a-1\right). Multiply \frac{4}{3a+3x-1} times \frac{3a-1}{3a-1}. Multiply \frac{4}{3a-1} times \frac{3x+3a-1}{3x+3a-1}.
\frac{\frac{4\left(3a-1\right)-4\left(3x+3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
Since \frac{4\left(3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)} and \frac{4\left(3x+3a-1\right)}{\left(3a-1\right)\left(3x+3a-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{12a-4-12x-12a+4}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
Do the multiplications in 4\left(3a-1\right)-4\left(3x+3a-1\right).
\frac{\frac{-12x}{\left(3a-1\right)\left(3x+3a-1\right)}}{x}
Combine like terms in 12a-4-12x-12a+4.
\frac{-12x}{\left(3a-1\right)\left(3x+3a-1\right)x}
Express \frac{\frac{-12x}{\left(3a-1\right)\left(3x+3a-1\right)}}{x} as a single fraction.
\frac{-12}{\left(3a-1\right)\left(3x+3a-1\right)}
Cancel out x in both numerator and denominator.
\frac{-12}{9ax+9a^{2}-3a-3x-3a+1}
Apply the distributive property by multiplying each term of 3a-1 by each term of 3x+3a-1.
\frac{-12}{9ax+9a^{2}-6a-3x+1}
Combine -3a and -3a to get -6a.
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}