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