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\frac{2}{a+1}+\frac{1}{3\left(a+1\right)}-\frac{4}{a+1}
Factor 3a+3.
\frac{2\times 3}{3\left(a+1\right)}+\frac{1}{3\left(a+1\right)}-\frac{4}{a+1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+1 and 3\left(a+1\right) is 3\left(a+1\right). Multiply \frac{2}{a+1} times \frac{3}{3}.
\frac{2\times 3+1}{3\left(a+1\right)}-\frac{4}{a+1}
Since \frac{2\times 3}{3\left(a+1\right)} and \frac{1}{3\left(a+1\right)} have the same denominator, add them by adding their numerators.
\frac{6+1}{3\left(a+1\right)}-\frac{4}{a+1}
Do the multiplications in 2\times 3+1.
\frac{7}{3\left(a+1\right)}-\frac{4}{a+1}
Do the calculations in 6+1.
\frac{7}{3\left(a+1\right)}-\frac{4\times 3}{3\left(a+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(a+1\right) and a+1 is 3\left(a+1\right). Multiply \frac{4}{a+1} times \frac{3}{3}.
\frac{7-4\times 3}{3\left(a+1\right)}
Since \frac{7}{3\left(a+1\right)} and \frac{4\times 3}{3\left(a+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{7-12}{3\left(a+1\right)}
Do the multiplications in 7-4\times 3.
\frac{-5}{3\left(a+1\right)}
Do the calculations in 7-12.
\frac{-5}{3a+3}
Expand 3\left(a+1\right).