Evaluate
\frac{1}{2}-\frac{5}{2x}
Expand
\frac{1}{2}-\frac{5}{2x}
Graph
Share
Copied to clipboard
\frac{\left(4x^{2}-25\right)\left(x-5\right)}{\left(2x^{2}+5x\right)\left(4x-10\right)}
Divide \frac{4x^{2}-25}{2x^{2}+5x} by \frac{4x-10}{x-5} by multiplying \frac{4x^{2}-25}{2x^{2}+5x} by the reciprocal of \frac{4x-10}{x-5}.
\frac{\left(x-5\right)\left(2x-5\right)\left(2x+5\right)}{2x\left(2x-5\right)\left(2x+5\right)}
Factor the expressions that are not already factored.
\frac{x-5}{2x}
Cancel out \left(2x-5\right)\left(2x+5\right) in both numerator and denominator.
\frac{\left(4x^{2}-25\right)\left(x-5\right)}{\left(2x^{2}+5x\right)\left(4x-10\right)}
Divide \frac{4x^{2}-25}{2x^{2}+5x} by \frac{4x-10}{x-5} by multiplying \frac{4x^{2}-25}{2x^{2}+5x} by the reciprocal of \frac{4x-10}{x-5}.
\frac{\left(x-5\right)\left(2x-5\right)\left(2x+5\right)}{2x\left(2x-5\right)\left(2x+5\right)}
Factor the expressions that are not already factored.
\frac{x-5}{2x}
Cancel out \left(2x-5\right)\left(2x+5\right) 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}