Question

Simplify into one fraction -2/x+3 - 4/x-5

Answer 1

You have to multiply each term by what it's missing for the denominators to both be the same.  The first term has x+3 but is missing x-5 so multiply top and bottom by x-5 and then distribute the numerator to -2x + 10.  Do the same for the other term that is missing the x+3 and distribute to get -(4x+12).  Distribute the negative in then simplify to get $\frac{-6x-2}{(x+3)(x-5)}$ or simplify even further to get $\frac{-2(3x+1)}{(x+3)(x-5)}$

Answer 2

Multiply and divide by the product of the denominators.
$\dfrac{-2}{x+3}+\dfrac{-4}{x-5}=\dfrac{-2(x-5)-4(x+3)}{(x+3)(x-5)}\\\\=\dfrac{-6x-2}{x^{2}-2x-15}$