How do you find the complex conjugate of 5-4i?

Simplify each rational expression. You will need to use factoring by grouping.
${\displaystyle \frac{x^2-2x+ax-2a}{x^2-2x+3ax-6a}}$

Find a solution to the equation
${\displaystyle \frac{1}{{\sin }^2\left(2x\right)}+\tan \left(x\right)-\frac{1}{\tan \left(x\right)}=2}$
Assuming ${\displaystyle \sin \left(x\right)\ne 0}$ and ${\displaystyle \cos \left(x\right)\ne 0}$, I simplified the above to
${\displaystyle 4{\sin }^2\left(x\right)-1-4\sin \left(x\right)\cos \left(x\right)=0}$
which is equivalent to
${\displaystyle \cos \left(2x\right)+\sin \left(2x\right)=\frac{1}{2}}$
I do not know what to do next. I would be grateful for any hints.

A gambling book recommends the following "winning strategy" for the game of roulette. It recommends that a gambler bet $1 onred. If red appears (which has probablity 18/38), then the gamblershould take her $1 profit and quit. If the gambler loses this bet (which has probablity 20/38 of occurring), she should make additional $1 bets on red on each of the next two spins of the roulette wheel and then quite. Let X denote the gamblers

Explain how to add complex numbers.
${\displaystyle 5+2i}$
${\displaystyle 8+7i}$

Is it possible to solve ${\displaystyle \cos \left(x\right)+2e^x=0}$ analytically?

Factor the trinomial. Note that the coefficient of ${\displaystyle x^2}$ is not equal to 1. ${\displaystyle 4x^2–3x=10.}$

What is the range of the function
${\displaystyle \frac{\sqrt{3}\sin x}{2+\cos x}}$