Question

Solve for w (see picture attached)

Answer 1

w = 4

Explanation:

Solve for 'w'.

To solve for 'w', first simplify the equation.

`\sf (1)/(w -5) + (5)/(w+3)=(2)/(w^2 - 2w - 15)`

`\sf (w + 3)/((w-5)(w+3))+(5*(w-5))/((w-5)(w+3))=(2)/(w^2-2w-15)\\\\\\ (w+3)/(w^2-5w+3w-15)+(5w-25)/(w^2-5w+3w-15)=(2)/(w^2-2w-15)\\\\\\`

`\sf (w +3 +5w-25)/(w^2-2w-15)=(2)/(w^2-2w-15)\\\\\\ (6w - 22)/(w^2-2w-15)=(2)/(w^2-2w-15)`

`\sf 6w-22 = (2)/((w^2-2w-15))*(w^2-22-15)`

6w - 22 = 2

Add 22 to both sides,

6w = 2 + 22

6w = 24

Divide both sides by 6,

w = 24/6

`\sf \boxed{\bf w = 4 }`