How do I factorize this numerator? $$\lim_{x\to -3}   \frac 1{x+3} + \frac 4{x^2+2x-3}$$
I have the solution I just need to know how i turn that into:
$$\frac {(x-1)+4}{(x+3)(x-1)}$$
I know this might be really simple but I'm not sure how to factorise the numerator.
Thanks in advance!

Look at the left hand term, and multiply both the numerator and denominator by $(x-1)$. Then both terms will have the same denominator (factor the denominator of the right-hand term), and the numerator of the left-hand term will be $(x-1)$ as required.
This is allowed since multiplying both the numerator and denominator by the same (non-zero) value is equivalent to multiplying by 1, which obviously does not change the value.
