Factor
\frac{2\cos(x)+\sqrt{2}-1}{2}
Evaluate
\frac{2\cos(x)+\sqrt{2}-1}{2}
Graph
Share
Copied to clipboard
factor(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\cos(x)-\frac{1}{2})
Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
factor(\frac{\sqrt{2}}{2}+\cos(x)-\frac{1}{2})
The square of \sqrt{2} is 2.
\frac{\sqrt{2}+2\cos(x)-1}{2}
Factor out \frac{1}{2}.
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}