Looking for some assistance from those who know LaTeX and what is wrong with the following equations to cause them to not render?

**Math Equation A:**

Code:

`[MATH]\frac{1}{2}\cdot \frac{\;\dfrac{(1+\sqrt{5})^n}{(1+\sqrt{5})^{n-1}} -\dfrac{1-\sqrt{5})^n}{(1+\sqrt{5})^{n-1}}\;} { \dfrac{(1+\sqrt{5})^{n-1}}{(1+\sqrt{5})^{n-1}} - \dfrac{(1-\sqrt{5})^{n-1}}{(1+\sqrt{5})^{n-1}}} \;=\; \frac{1}{2}\cdot\frac{(1 + \sqrt{5}) - (1-\sqrt{5})\left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}} {1 - \left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}}}[/MATH]`

**Math Equation B:**

Code:

`[MATH]\lim_{n\to\infty}\frac{F_n}{F_{n-1}} \;=\;\lim_{n\to\infty} \frac{1}{2}\cdot\frac{(1 + \sqrt{5}) - (1-\sqrt{5})\left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}} {1 - \left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}}}[/MATH]`

\(\displaystyle \frac{1}{2}\cdot \frac{\;\dfrac{(1+\sqrt{5})^n}{(1+\sqrt{5})^{n-1}} -\dfrac{1-\sqrt{5})^n}{(1+\sqrt{5})^{n-1}}\;} { \dfrac{(1+\sqrt{5})^{n-1}}{(1+\sqrt{5})^{n-1}} - \dfrac{(1-\sqrt{5})^{n-1}}{(1+\sqrt{5})^{n-1}}} \;=\; \frac{1}{2}\cdot\frac{(1 + \sqrt{5}) - (1-\sqrt{5})\left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}} {1 - \left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}}}\)

\(\displaystyle \lim_{n\to\infty}\frac{F_n}{F_{n-1}} \;=\;\lim_{n\to\infty} \frac{1}{2}\cdot\frac{(1 + \sqrt{5}) - (1-\sqrt{5})\left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}} {1 - \left(\dfrac{1-\sqrt{5}}{1+\sqrt{5}}\right)^{n-1}}}\)

Thanks in advance.