Answer:
w = 4
Step-by-step explanation:
Solve for 'w'.
To solve for 'w', first simplify the equation.
[tex]\sf \dfrac{1}{w -5} + \dfrac{5}{w+3}=\dfrac{2}{w^2 - 2w - 15}[/tex]
[tex]\sf \dfrac{w + 3}{(w-5)(w+3)}+\dfrac{5*(w-5)}{(w-5)(w+3)}=\dfrac{2}{w^2-2w-15}\\\\\\ \dfrac{w+3}{w^2-5w+3w-15}+\dfrac{5w-25}{w^2-5w+3w-15}=\dfrac{2}{w^2-2w-15}\\\\\\[/tex]
[tex]\sf \dfrac{w +3 +5w-25}{w^2-2w-15}=\dfrac{2}{w^2-2w-15}\\\\\\ \dfrac{6w - 22}{w^2-2w-15}=\dfrac{2}{w^2-2w-15}[/tex]
[tex]\sf 6w-22 = \dfrac{2}{(w^2-2w-15)}*(w^2-22-15)[/tex]
6w - 22 = 2
Add 22 to both sides,
6w = 2 + 22
6w = 24
Divide both sides by 6,
w = 24/6
[tex]\sf \boxed{\bf w = 4 }[/tex]
