To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+1$ and $x-1$ is $\left(x-1\right)\left(x+1\right)$. Multiply $\frac{1}{x+1}$ times $\frac{x-1}{x-1}$. Multiply $\frac{1}{x-1}$ times $\frac{x+1}{x+1}$.
Since $\frac{x-1}{\left(x-1\right)\left(x+1\right)}$ and $\frac{x+1}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
Since $\frac{-2}{\left(x-1\right)\left(x+1\right)}$ and $\frac{3}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, add them by adding their numerators. Add $-2$ and $3$ to get $1$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+1$ and $x-1$ is $\left(x-1\right)\left(x+1\right)$. Multiply $\frac{1}{x+1}$ times $\frac{x-1}{x-1}$. Multiply $\frac{1}{x-1}$ times $\frac{x+1}{x+1}$.
Since $\frac{x-1}{\left(x-1\right)\left(x+1\right)}$ and $\frac{x+1}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
Since $\frac{-2}{\left(x-1\right)\left(x+1\right)}$ and $\frac{3}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, add them by adding their numerators. Add $-2$ and $3$ to get $1$.
Consider $\left(x-1\right)\left(x+1\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $1$.
If $F$ is the composition of two differentiable functions $f\left(u\right)$ and $u=g\left(x\right)$, that is, if $F\left(x\right)=f\left(g\left(x\right)\right)$, then the derivative of $F$ is the derivative of $f$ with respect to $u$ times the derivative of $g$ with respect to $x$, that is, $\frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right)$.
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.
