Evaluate
\frac{3x\beta +2x-2}{x\left(x-1\right)}
Differentiate w.r.t. x
\frac{-3\beta x^{2}-2x^{2}+4x-2}{\left(x\left(x-1\right)\right)^{2}}
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\frac{2}{x}+\frac{3\beta }{x-1}
Express \frac{3}{x-1}\beta as a single fraction.
\frac{2\left(x-1\right)}{x\left(x-1\right)}+\frac{3\beta x}{x\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x-1 is x\left(x-1\right). Multiply \frac{2}{x} times \frac{x-1}{x-1}. Multiply \frac{3\beta }{x-1} times \frac{x}{x}.
\frac{2\left(x-1\right)+3\beta x}{x\left(x-1\right)}
Since \frac{2\left(x-1\right)}{x\left(x-1\right)} and \frac{3\beta x}{x\left(x-1\right)} have the same denominator, add them by adding their numerators.
\frac{2x-2+3\beta x}{x\left(x-1\right)}
Do the multiplications in 2\left(x-1\right)+3\beta x.
\frac{2x-2+3\beta x}{x^{2}-x}
Expand x\left(x-1\right).
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Limits
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