Express the equation as a single fraction in its simplest form Express the equation
$$ 4 - \left( (x + 3) ÷ {\frac {x² + 5x + 6}{x - 2}} \right) $$
as a single fraction in its simplest form.
So far all I managed to do was factorise the numerator to get this $$(x + 3)(x + 2)$$
Where do I go from here?

Well here is an answer for if the expression is as I have written it in my comment above. If my comment indeed has the wrong expression, then the steps are similar, but involves a closer look using the proper order of operations.
We first use the fact that $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$ where $b,c,d\neq 0$. This yields
$$\begin{align}4-\left((x+3)\div\frac{x^2+5x+6}{x-2}\right)&=4-\left((x+3)\times\frac{x-2}{x^2+5x+6}\right)\\&=4-\left(\frac{(x+3)(x-2)}{x^2+5x+6}\right)\end{align}$$
Now use your factorization $x^2+5x+6=(x+2)(x+3)$ and do the appropriate cancellations. Then I'll leave the rest for you to deal with.
Recall: $4-\frac{a}{b}=\frac{4b-a}{b}$ and $\frac{ab}{bc}=\frac{a}{c}$ if $b,c\neq 0$.
