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