Evaluate
\frac{3b+31}{5\left(b+2\right)}
Expand
\frac{3b+31}{5\left(b+2\right)}
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\frac{3}{5}+\frac{5\left(b-1\right)}{\left(b-1\right)\left(b+2\right)}
Factor the expressions that are not already factored in \frac{5b-5}{b^{2}+b-2}.
\frac{3}{5}+\frac{5}{b+2}
Cancel out b-1 in both numerator and denominator.
\frac{3\left(b+2\right)}{5\left(b+2\right)}+\frac{5\times 5}{5\left(b+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and b+2 is 5\left(b+2\right). Multiply \frac{3}{5} times \frac{b+2}{b+2}. Multiply \frac{5}{b+2} times \frac{5}{5}.
\frac{3\left(b+2\right)+5\times 5}{5\left(b+2\right)}
Since \frac{3\left(b+2\right)}{5\left(b+2\right)} and \frac{5\times 5}{5\left(b+2\right)} have the same denominator, add them by adding their numerators.
\frac{3b+6+25}{5\left(b+2\right)}
Do the multiplications in 3\left(b+2\right)+5\times 5.
\frac{3b+31}{5\left(b+2\right)}
Combine like terms in 3b+6+25.
\frac{3b+31}{5b+10}
Expand 5\left(b+2\right).
\frac{3}{5}+\frac{5\left(b-1\right)}{\left(b-1\right)\left(b+2\right)}
Factor the expressions that are not already factored in \frac{5b-5}{b^{2}+b-2}.
\frac{3}{5}+\frac{5}{b+2}
Cancel out b-1 in both numerator and denominator.
\frac{3\left(b+2\right)}{5\left(b+2\right)}+\frac{5\times 5}{5\left(b+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and b+2 is 5\left(b+2\right). Multiply \frac{3}{5} times \frac{b+2}{b+2}. Multiply \frac{5}{b+2} times \frac{5}{5}.
\frac{3\left(b+2\right)+5\times 5}{5\left(b+2\right)}
Since \frac{3\left(b+2\right)}{5\left(b+2\right)} and \frac{5\times 5}{5\left(b+2\right)} have the same denominator, add them by adding their numerators.
\frac{3b+6+25}{5\left(b+2\right)}
Do the multiplications in 3\left(b+2\right)+5\times 5.
\frac{3b+31}{5\left(b+2\right)}
Combine like terms in 3b+6+25.
\frac{3b+31}{5b+10}
Expand 5\left(b+2\right).
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