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