Evaluate
\frac{x+1}{2\left(2x+1\right)}
Expand
\frac{x+1}{2\left(2x+1\right)}
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\frac{1}{3+\frac{x-1}{x+1}}
Anything divided by one gives itself.
\frac{1}{\frac{3\left(x+1\right)}{x+1}+\frac{x-1}{x+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+1}{x+1}.
\frac{1}{\frac{3\left(x+1\right)+x-1}{x+1}}
Since \frac{3\left(x+1\right)}{x+1} and \frac{x-1}{x+1} have the same denominator, add them by adding their numerators.
\frac{1}{\frac{3x+3+x-1}{x+1}}
Do the multiplications in 3\left(x+1\right)+x-1.
\frac{1}{\frac{4x+2}{x+1}}
Combine like terms in 3x+3+x-1.
\frac{x+1}{4x+2}
Divide 1 by \frac{4x+2}{x+1} by multiplying 1 by the reciprocal of \frac{4x+2}{x+1}.
\frac{1}{3+\frac{x-1}{x+1}}
Anything divided by one gives itself.
\frac{1}{\frac{3\left(x+1\right)}{x+1}+\frac{x-1}{x+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+1}{x+1}.
\frac{1}{\frac{3\left(x+1\right)+x-1}{x+1}}
Since \frac{3\left(x+1\right)}{x+1} and \frac{x-1}{x+1} have the same denominator, add them by adding their numerators.
\frac{1}{\frac{3x+3+x-1}{x+1}}
Do the multiplications in 3\left(x+1\right)+x-1.
\frac{1}{\frac{4x+2}{x+1}}
Combine like terms in 3x+3+x-1.
\frac{x+1}{4x+2}
Divide 1 by \frac{4x+2}{x+1} by multiplying 1 by the reciprocal of \frac{4x+2}{x+1}.
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}