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