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