Skip to main content
Evaluate
Tick mark Image
Expand
Tick mark Image
Graph

Similar Problems from Web Search

Share

\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.