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-2x-6
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Polynomial
5 problems similar to:
( x + 2 + \frac { 5 } { 2 - x } ) \div \frac { 3 - x } { 2 x - 4 }
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\frac{\frac{\left(x+2\right)\left(2-x\right)}{2-x}+\frac{5}{2-x}}{\frac{3-x}{2x-4}}
To add or subtract expressions, expand them to make their denominators the same. Multiply x+2 times \frac{2-x}{2-x}.
\frac{\frac{\left(x+2\right)\left(2-x\right)+5}{2-x}}{\frac{3-x}{2x-4}}
Since \frac{\left(x+2\right)\left(2-x\right)}{2-x} and \frac{5}{2-x} have the same denominator, add them by adding their numerators.
\frac{\frac{2x-x^{2}+4-2x+5}{2-x}}{\frac{3-x}{2x-4}}
Do the multiplications in \left(x+2\right)\left(2-x\right)+5.
\frac{\frac{-x^{2}+9}{2-x}}{\frac{3-x}{2x-4}}
Combine like terms in 2x-x^{2}+4-2x+5.
\frac{\left(-x^{2}+9\right)\left(2x-4\right)}{\left(2-x\right)\left(3-x\right)}
Divide \frac{-x^{2}+9}{2-x} by \frac{3-x}{2x-4} by multiplying \frac{-x^{2}+9}{2-x} by the reciprocal of \frac{3-x}{2x-4}.
\frac{2\left(x-3\right)\left(x-2\right)\left(-x-3\right)}{\left(-x+2\right)\left(-x+3\right)}
Factor the expressions that are not already factored.
\frac{-\left(-1\right)\times 2\left(-x-3\right)\left(-x+2\right)\left(-x+3\right)}{\left(-x+2\right)\left(-x+3\right)}
Extract the negative sign in -3+x. Extract the negative sign in -2+x.
-\left(-1\right)\times 2\left(-x-3\right)
Cancel out \left(-x+2\right)\left(-x+3\right) in both numerator and denominator.
-2x-6
Expand the expression.
\frac{\frac{\left(x+2\right)\left(2-x\right)}{2-x}+\frac{5}{2-x}}{\frac{3-x}{2x-4}}
To add or subtract expressions, expand them to make their denominators the same. Multiply x+2 times \frac{2-x}{2-x}.
\frac{\frac{\left(x+2\right)\left(2-x\right)+5}{2-x}}{\frac{3-x}{2x-4}}
Since \frac{\left(x+2\right)\left(2-x\right)}{2-x} and \frac{5}{2-x} have the same denominator, add them by adding their numerators.
\frac{\frac{2x-x^{2}+4-2x+5}{2-x}}{\frac{3-x}{2x-4}}
Do the multiplications in \left(x+2\right)\left(2-x\right)+5.
\frac{\frac{-x^{2}+9}{2-x}}{\frac{3-x}{2x-4}}
Combine like terms in 2x-x^{2}+4-2x+5.
\frac{\left(-x^{2}+9\right)\left(2x-4\right)}{\left(2-x\right)\left(3-x\right)}
Divide \frac{-x^{2}+9}{2-x} by \frac{3-x}{2x-4} by multiplying \frac{-x^{2}+9}{2-x} by the reciprocal of \frac{3-x}{2x-4}.
\frac{2\left(x-3\right)\left(x-2\right)\left(-x-3\right)}{\left(-x+2\right)\left(-x+3\right)}
Factor the expressions that are not already factored.
\frac{-\left(-1\right)\times 2\left(-x-3\right)\left(-x+2\right)\left(-x+3\right)}{\left(-x+2\right)\left(-x+3\right)}
Extract the negative sign in -3+x. Extract the negative sign in -2+x.
-\left(-1\right)\times 2\left(-x-3\right)
Cancel out \left(-x+2\right)\left(-x+3\right) in both numerator and denominator.
-2x-6
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}