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5 problems similar to:
2 x + \frac { 3 } { 2 x - 4 } - ( 3 + \frac { 3 } { 2 x - 4 } )
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2x+\frac{3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
Factor 2x-4.
\frac{2x\times 2\left(x-2\right)}{2\left(x-2\right)}+\frac{3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2\left(x-2\right)}{2\left(x-2\right)}.
\frac{2x\times 2\left(x-2\right)+3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
Since \frac{2x\times 2\left(x-2\right)}{2\left(x-2\right)} and \frac{3}{2\left(x-2\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
Do the multiplications in 2x\times 2\left(x-2\right)+3.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2\left(x-2\right)}\right)
Factor 2x-4.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(\frac{3\times 2\left(x-2\right)}{2\left(x-2\right)}+\frac{3}{2\left(x-2\right)}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2\left(x-2\right)}{2\left(x-2\right)}.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{3\times 2\left(x-2\right)+3}{2\left(x-2\right)}
Since \frac{3\times 2\left(x-2\right)}{2\left(x-2\right)} and \frac{3}{2\left(x-2\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-12+3}{2\left(x-2\right)}
Do the multiplications in 3\times 2\left(x-2\right)+3.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-9}{2\left(x-2\right)}
Combine like terms in 6x-12+3.
\frac{4x^{2}-8x+3-\left(6x-9\right)}{2\left(x-2\right)}
Since \frac{4x^{2}-8x+3}{2\left(x-2\right)} and \frac{6x-9}{2\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-8x+3-6x+9}{2\left(x-2\right)}
Do the multiplications in 4x^{2}-8x+3-\left(6x-9\right).
\frac{4x^{2}-14x+12}{2\left(x-2\right)}
Combine like terms in 4x^{2}-8x+3-6x+9.
\frac{2\left(x-2\right)\left(2x-3\right)}{2\left(x-2\right)}
Factor the expressions that are not already factored in \frac{4x^{2}-14x+12}{2\left(x-2\right)}.
2x-3
Cancel out 2\left(x-2\right) in both numerator and denominator.
2x+\frac{3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
Factor 2x-4.
\frac{2x\times 2\left(x-2\right)}{2\left(x-2\right)}+\frac{3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2\left(x-2\right)}{2\left(x-2\right)}.
\frac{2x\times 2\left(x-2\right)+3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
Since \frac{2x\times 2\left(x-2\right)}{2\left(x-2\right)} and \frac{3}{2\left(x-2\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)
Do the multiplications in 2x\times 2\left(x-2\right)+3.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2\left(x-2\right)}\right)
Factor 2x-4.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(\frac{3\times 2\left(x-2\right)}{2\left(x-2\right)}+\frac{3}{2\left(x-2\right)}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2\left(x-2\right)}{2\left(x-2\right)}.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{3\times 2\left(x-2\right)+3}{2\left(x-2\right)}
Since \frac{3\times 2\left(x-2\right)}{2\left(x-2\right)} and \frac{3}{2\left(x-2\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-12+3}{2\left(x-2\right)}
Do the multiplications in 3\times 2\left(x-2\right)+3.
\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-9}{2\left(x-2\right)}
Combine like terms in 6x-12+3.
\frac{4x^{2}-8x+3-\left(6x-9\right)}{2\left(x-2\right)}
Since \frac{4x^{2}-8x+3}{2\left(x-2\right)} and \frac{6x-9}{2\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-8x+3-6x+9}{2\left(x-2\right)}
Do the multiplications in 4x^{2}-8x+3-\left(6x-9\right).
\frac{4x^{2}-14x+12}{2\left(x-2\right)}
Combine like terms in 4x^{2}-8x+3-6x+9.
\frac{2\left(x-2\right)\left(2x-3\right)}{2\left(x-2\right)}
Factor the expressions that are not already factored in \frac{4x^{2}-14x+12}{2\left(x-2\right)}.
2x-3
Cancel out 2\left(x-2\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}