Evaluate
\frac{x\left(x-1\right)}{x^{2}-25}
Factor
\frac{x\left(x-1\right)}{x^{2}-25}
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\frac{4x}{\left(x-5\right)\left(x+5\right)}+\frac{x}{x+5}
Factor x^{2}-25.
\frac{4x}{\left(x-5\right)\left(x+5\right)}+\frac{x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x+5 is \left(x-5\right)\left(x+5\right). Multiply \frac{x}{x+5} times \frac{x-5}{x-5}.
\frac{4x+x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}
Since \frac{4x}{\left(x-5\right)\left(x+5\right)} and \frac{x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{4x+x^{2}-5x}{\left(x-5\right)\left(x+5\right)}
Do the multiplications in 4x+x\left(x-5\right).
\frac{-x+x^{2}}{\left(x-5\right)\left(x+5\right)}
Combine like terms in 4x+x^{2}-5x.
\frac{-x+x^{2}}{x^{2}-25}
Expand \left(x-5\right)\left(x+5\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}