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