Evaluate
\frac{x+6}{x+1}
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\frac{x+6}{x+1}
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\frac{x\left(x^{2}+6x+9\right)}{\left(x+3\right)\left(x^{2}+x\right)}+\frac{3x-3}{x^{2}-1}
Divide \frac{x}{x+3} by \frac{x^{2}+x}{x^{2}+6x+9} by multiplying \frac{x}{x+3} by the reciprocal of \frac{x^{2}+x}{x^{2}+6x+9}.
\frac{x\left(x+3\right)^{2}}{x\left(x+1\right)\left(x+3\right)}+\frac{3x-3}{x^{2}-1}
Factor the expressions that are not already factored in \frac{x\left(x^{2}+6x+9\right)}{\left(x+3\right)\left(x^{2}+x\right)}.
\frac{x+3}{x+1}+\frac{3x-3}{x^{2}-1}
Cancel out x\left(x+3\right) in both numerator and denominator.
\frac{x+3}{x+1}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{3x-3}{x^{2}-1}.
\frac{x+3}{x+1}+\frac{3}{x+1}
Cancel out x-1 in both numerator and denominator.
\frac{x+3+3}{x+1}
Since \frac{x+3}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators.
\frac{x+6}{x+1}
Combine like terms in x+3+3.
\frac{x\left(x^{2}+6x+9\right)}{\left(x+3\right)\left(x^{2}+x\right)}+\frac{3x-3}{x^{2}-1}
Divide \frac{x}{x+3} by \frac{x^{2}+x}{x^{2}+6x+9} by multiplying \frac{x}{x+3} by the reciprocal of \frac{x^{2}+x}{x^{2}+6x+9}.
\frac{x\left(x+3\right)^{2}}{x\left(x+1\right)\left(x+3\right)}+\frac{3x-3}{x^{2}-1}
Factor the expressions that are not already factored in \frac{x\left(x^{2}+6x+9\right)}{\left(x+3\right)\left(x^{2}+x\right)}.
\frac{x+3}{x+1}+\frac{3x-3}{x^{2}-1}
Cancel out x\left(x+3\right) in both numerator and denominator.
\frac{x+3}{x+1}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{3x-3}{x^{2}-1}.
\frac{x+3}{x+1}+\frac{3}{x+1}
Cancel out x-1 in both numerator and denominator.
\frac{x+3+3}{x+1}
Since \frac{x+3}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators.
\frac{x+6}{x+1}
Combine like terms in x+3+3.
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Limits
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