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\frac{4x-5}{4\left(3x+1\right)}+\frac{3x-1}{3x+1}
Factor 12x+4.
\frac{4x-5}{4\left(3x+1\right)}+\frac{4\left(3x-1\right)}{4\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(3x+1\right) and 3x+1 is 4\left(3x+1\right). Multiply \frac{3x-1}{3x+1} times \frac{4}{4}.
\frac{4x-5+4\left(3x-1\right)}{4\left(3x+1\right)}
Since \frac{4x-5}{4\left(3x+1\right)} and \frac{4\left(3x-1\right)}{4\left(3x+1\right)} have the same denominator, add them by adding their numerators.
\frac{4x-5+12x-4}{4\left(3x+1\right)}
Do the multiplications in 4x-5+4\left(3x-1\right).
\frac{16x-9}{4\left(3x+1\right)}
Combine like terms in 4x-5+12x-4.
\frac{16x-9}{12x+4}
Expand 4\left(3x+1\right).
\frac{4x-5}{4\left(3x+1\right)}+\frac{3x-1}{3x+1}
Factor 12x+4.
\frac{4x-5}{4\left(3x+1\right)}+\frac{4\left(3x-1\right)}{4\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(3x+1\right) and 3x+1 is 4\left(3x+1\right). Multiply \frac{3x-1}{3x+1} times \frac{4}{4}.
\frac{4x-5+4\left(3x-1\right)}{4\left(3x+1\right)}
Since \frac{4x-5}{4\left(3x+1\right)} and \frac{4\left(3x-1\right)}{4\left(3x+1\right)} have the same denominator, add them by adding their numerators.
\frac{4x-5+12x-4}{4\left(3x+1\right)}
Do the multiplications in 4x-5+4\left(3x-1\right).
\frac{16x-9}{4\left(3x+1\right)}
Combine like terms in 4x-5+12x-4.
\frac{16x-9}{12x+4}
Expand 4\left(3x+1\right).