Evaluate
\frac{3\left(x-2\right)}{4\left(3-x\right)}
Expand
-\frac{3\left(x-2\right)}{4\left(x-3\right)}
Graph
Share
Copied to clipboard
\frac{\frac{3}{2}\times \frac{\left(x+3\right)\left(x-2\right)}{12-4x}}{\frac{x+3}{2}}
Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.
\frac{\frac{3\left(x+3\right)\left(x-2\right)}{2\left(12-4x\right)}}{\frac{x+3}{2}}
Multiply \frac{3}{2} times \frac{\left(x+3\right)\left(x-2\right)}{12-4x} by multiplying numerator times numerator and denominator times denominator.
\frac{3\left(x+3\right)\left(x-2\right)\times 2}{2\left(12-4x\right)\left(x+3\right)}
Divide \frac{3\left(x+3\right)\left(x-2\right)}{2\left(12-4x\right)} by \frac{x+3}{2} by multiplying \frac{3\left(x+3\right)\left(x-2\right)}{2\left(12-4x\right)} by the reciprocal of \frac{x+3}{2}.
\frac{3\left(x-2\right)}{-4x+12}
Cancel out 2\left(x+3\right) in both numerator and denominator.
\frac{3x-6}{-4x+12}
Use the distributive property to multiply 3 by x-2.
\frac{\frac{3}{2}\times \frac{\left(x+3\right)\left(x-2\right)}{12-4x}}{\frac{x+3}{2}}
Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.
\frac{\frac{3\left(x+3\right)\left(x-2\right)}{2\left(12-4x\right)}}{\frac{x+3}{2}}
Multiply \frac{3}{2} times \frac{\left(x+3\right)\left(x-2\right)}{12-4x} by multiplying numerator times numerator and denominator times denominator.
\frac{3\left(x+3\right)\left(x-2\right)\times 2}{2\left(12-4x\right)\left(x+3\right)}
Divide \frac{3\left(x+3\right)\left(x-2\right)}{2\left(12-4x\right)} by \frac{x+3}{2} by multiplying \frac{3\left(x+3\right)\left(x-2\right)}{2\left(12-4x\right)} by the reciprocal of \frac{x+3}{2}.
\frac{3\left(x-2\right)}{-4x+12}
Cancel out 2\left(x+3\right) in both numerator and denominator.
\frac{3x-6}{-4x+12}
Use the distributive property to multiply 3 by x-2.
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}