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\frac{22x\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}+\frac{b\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x+3\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right)\left(x+3\right). Multiply \frac{22x}{x-1} times \frac{\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x+3\right)}. Multiply \frac{b}{\left(x+3\right)\left(x+1\right)} times \frac{x-1}{x-1}.
\frac{22x\left(x+1\right)\left(x+3\right)+b\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Since \frac{22x\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} and \frac{b\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{22x^{3}+66x^{2}+22x^{2}+66x+bx-b}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Do the multiplications in 22x\left(x+1\right)\left(x+3\right)+b\left(x-1\right).
\frac{22x^{3}+88x^{2}+66x+bx-b}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Combine like terms in 22x^{3}+66x^{2}+22x^{2}+66x+bx-b.
\frac{22x^{3}+88x^{2}+66x+bx-b}{x^{3}+3x^{2}-x-3}
Expand \left(x-1\right)\left(x+1\right)\left(x+3\right).
\frac{22x\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}+\frac{b\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x+3\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right)\left(x+3\right). Multiply \frac{22x}{x-1} times \frac{\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x+3\right)}. Multiply \frac{b}{\left(x+3\right)\left(x+1\right)} times \frac{x-1}{x-1}.
\frac{22x\left(x+1\right)\left(x+3\right)+b\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Since \frac{22x\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} and \frac{b\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{22x^{3}+66x^{2}+22x^{2}+66x+bx-b}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Do the multiplications in 22x\left(x+1\right)\left(x+3\right)+b\left(x-1\right).
\frac{22x^{3}+88x^{2}+66x+bx-b}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Combine like terms in 22x^{3}+66x^{2}+22x^{2}+66x+bx-b.
\frac{22x^{3}+88x^{2}+66x+bx-b}{x^{3}+3x^{2}-x-3}
Expand \left(x-1\right)\left(x+1\right)\left(x+3\right).