Evaluate
\frac{4x\left(x-3\right)}{3x-4}
Expand
\frac{4\left(x^{2}-3x\right)}{3x-4}
Graph
Quiz
Polynomial
5 problems similar to:
\frac { 12 } { \frac { x + 2 } { x - 3 } - \frac { x - 4 } { x } }
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\frac{12}{\frac{\left(x+2\right)x}{x\left(x-3\right)}-\frac{\left(x-4\right)\left(x-3\right)}{x\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+2}{x-3} times \frac{x}{x}. Multiply \frac{x-4}{x} times \frac{x-3}{x-3}.
\frac{12}{\frac{\left(x+2\right)x-\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)}}
Since \frac{\left(x+2\right)x}{x\left(x-3\right)} and \frac{\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12}{\frac{x^{2}+2x-x^{2}+3x+4x-12}{x\left(x-3\right)}}
Do the multiplications in \left(x+2\right)x-\left(x-4\right)\left(x-3\right).
\frac{12}{\frac{9x-12}{x\left(x-3\right)}}
Combine like terms in x^{2}+2x-x^{2}+3x+4x-12.
\frac{12x\left(x-3\right)}{9x-12}
Divide 12 by \frac{9x-12}{x\left(x-3\right)} by multiplying 12 by the reciprocal of \frac{9x-12}{x\left(x-3\right)}.
\frac{12x\left(x-3\right)}{3\left(3x-4\right)}
Factor the expressions that are not already factored.
\frac{4x\left(x-3\right)}{3x-4}
Cancel out 3 in both numerator and denominator.
\frac{4x^{2}-12x}{3x-4}
Expand the expression.
\frac{12}{\frac{\left(x+2\right)x}{x\left(x-3\right)}-\frac{\left(x-4\right)\left(x-3\right)}{x\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+2}{x-3} times \frac{x}{x}. Multiply \frac{x-4}{x} times \frac{x-3}{x-3}.
\frac{12}{\frac{\left(x+2\right)x-\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)}}
Since \frac{\left(x+2\right)x}{x\left(x-3\right)} and \frac{\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12}{\frac{x^{2}+2x-x^{2}+3x+4x-12}{x\left(x-3\right)}}
Do the multiplications in \left(x+2\right)x-\left(x-4\right)\left(x-3\right).
\frac{12}{\frac{9x-12}{x\left(x-3\right)}}
Combine like terms in x^{2}+2x-x^{2}+3x+4x-12.
\frac{12x\left(x-3\right)}{9x-12}
Divide 12 by \frac{9x-12}{x\left(x-3\right)} by multiplying 12 by the reciprocal of \frac{9x-12}{x\left(x-3\right)}.
\frac{12x\left(x-3\right)}{3\left(3x-4\right)}
Factor the expressions that are not already factored.
\frac{4x\left(x-3\right)}{3x-4}
Cancel out 3 in both numerator and denominator.
\frac{4x^{2}-12x}{3x-4}
Expand the expression.
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}