Consider $\left(1+3\sqrt{5}\right)\left(1-3\sqrt{5}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Consider $\left(1-3\sqrt{5}\right)\left(1+3\sqrt{5}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Consider $\left(2\sqrt{3}+1\right)\left(2\sqrt{3}-1\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Consider $\left(2\sqrt{3}-1\right)\left(2\sqrt{3}+1\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $44$ and $11$ is $44$. Multiply $\frac{2\sqrt{3}-1}{11}$ times $\frac{4}{4}$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $44$ and $11$ is $44$. Multiply $\frac{2\sqrt{3}+1}{11}$ times $\frac{4}{4}$.
