To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $4x^{2}-2x+1$ and $\left(2x+1\right)\left(4x^{2}-2x+1\right)$ is $\left(2x+1\right)\left(4x^{2}-2x+1\right)$. Multiply $\frac{x+2}{4x^{2}-2x+1}$ times $\frac{2x+1}{2x+1}$.
Since $\frac{\left(x+2\right)\left(2x+1\right)}{\left(2x+1\right)\left(4x^{2}-2x+1\right)}$ and $\frac{8x+1}{\left(2x+1\right)\left(4x^{2}-2x+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $4x^{2}-2x+1$ and $\left(2x+1\right)\left(4x^{2}-2x+1\right)$ is $\left(2x+1\right)\left(4x^{2}-2x+1\right)$. Multiply $\frac{x+2}{4x^{2}-2x+1}$ times $\frac{2x+1}{2x+1}$.
Since $\frac{\left(x+2\right)\left(2x+1\right)}{\left(2x+1\right)\left(4x^{2}-2x+1\right)}$ and $\frac{8x+1}{\left(2x+1\right)\left(4x^{2}-2x+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
