Evaluate
\frac{x+3}{x-1}
Expand
\frac{x+3}{x-1}
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\frac{\left(2x^{2}+17x+8\right)\left(x+3\right)^{2}}{\left(x^{2}+11x+24\right)\left(2x^{2}-x-1\right)}
Divide \frac{2x^{2}+17x+8}{x^{2}+11x+24} by \frac{2x^{2}-x-1}{\left(x+3\right)^{2}} by multiplying \frac{2x^{2}+17x+8}{x^{2}+11x+24} by the reciprocal of \frac{2x^{2}-x-1}{\left(x+3\right)^{2}}.
\frac{\left(x+8\right)\left(2x+1\right)\left(x+3\right)^{2}}{\left(x-1\right)\left(x+3\right)\left(x+8\right)\left(2x+1\right)}
Factor the expressions that are not already factored.
\frac{x+3}{x-1}
Cancel out \left(x+3\right)\left(x+8\right)\left(2x+1\right) in both numerator and denominator.
\frac{\left(2x^{2}+17x+8\right)\left(x+3\right)^{2}}{\left(x^{2}+11x+24\right)\left(2x^{2}-x-1\right)}
Divide \frac{2x^{2}+17x+8}{x^{2}+11x+24} by \frac{2x^{2}-x-1}{\left(x+3\right)^{2}} by multiplying \frac{2x^{2}+17x+8}{x^{2}+11x+24} by the reciprocal of \frac{2x^{2}-x-1}{\left(x+3\right)^{2}}.
\frac{\left(x+8\right)\left(2x+1\right)\left(x+3\right)^{2}}{\left(x-1\right)\left(x+3\right)\left(x+8\right)\left(2x+1\right)}
Factor the expressions that are not already factored.
\frac{x+3}{x-1}
Cancel out \left(x+3\right)\left(x+8\right)\left(2x+1\right) in both numerator and denominator.
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