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\frac{\left(x+1\right)\times 2}{9\left(5x+5\right)}
Divide \frac{x+1}{9} by \frac{5x+5}{2} by multiplying \frac{x+1}{9} by the reciprocal of \frac{5x+5}{2}.
\frac{2\left(x+1\right)}{5\times 9\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{2}{5\times 9}
Cancel out x+1 in both numerator and denominator.
\frac{2}{45}
Multiply 5 and 9 to get 45.