Solve for $x$.
$$1-\frac{1}{1-\frac{1}{1-x}}=n$$
Give your answer in terms of $n$.

Solve the following simultaneous equation.
$$\begin{cases} \frac{3}{x+y}+\frac{2}{x-y}=-1 \\ \frac{9}{x+y}-\frac{5}{x-y}=-14 \end{cases}$$

Simplify the following:

*Give your answer in the form $-\frac{x^n-a}{x^m+b}$ where $a, b, m, n$ are integers.

Simplify the following:

a) Solve for $x$.
$$\frac{x+2018}{2019}=\frac{x+2019}{2018}$$
b) Solve for $x$. Give your answers in terms of $a$.
$$\frac{x+a}{a+1}=\frac{x+\left(a+1\right)}{a}$$

Rearrange and simplify $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$ to make $u$ the subject. Your answer should be a single fraction.

Simplify $\left(x\div\left(y\div z\right)\right)\div\left(\left(x\div y\right)\div z\right)$.