Evaluate
\frac{2a+3}{a-1}
Expand
\frac{2a+3}{a-1}
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\frac{3\left(a-1\right)\left(a+1\right)}{\left(a-1\right)^{2}}-\frac{a}{a-1}
Factor the expressions that are not already factored in \frac{3a^{2}-3}{a^{2}-2a+1}.
\frac{3\left(a+1\right)}{a-1}-\frac{a}{a-1}
Cancel out a-1 in both numerator and denominator.
\frac{3\left(a+1\right)-a}{a-1}
Since \frac{3\left(a+1\right)}{a-1} and \frac{a}{a-1} have the same denominator, subtract them by subtracting their numerators.
\frac{3a+3-a}{a-1}
Do the multiplications in 3\left(a+1\right)-a.
\frac{2a+3}{a-1}
Combine like terms in 3a+3-a.
\frac{3\left(a-1\right)\left(a+1\right)}{\left(a-1\right)^{2}}-\frac{a}{a-1}
Factor the expressions that are not already factored in \frac{3a^{2}-3}{a^{2}-2a+1}.
\frac{3\left(a+1\right)}{a-1}-\frac{a}{a-1}
Cancel out a-1 in both numerator and denominator.
\frac{3\left(a+1\right)-a}{a-1}
Since \frac{3\left(a+1\right)}{a-1} and \frac{a}{a-1} have the same denominator, subtract them by subtracting their numerators.
\frac{3a+3-a}{a-1}
Do the multiplications in 3\left(a+1\right)-a.
\frac{2a+3}{a-1}
Combine like terms in 3a+3-a.
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