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6/y+4 + 1 = 5/2y+8

step by step solve the equations 

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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You should put parentheses around to avoid confusion!

6/(y+4)+1=5/(2y+8)

Notice that 2y+8=2*(y+4). Therefore, we can move 5/(2y+8) to the left, by changing its sign and writing it on the left with minus sign. We can also move 1 to the right, again, with sign change.

6/(y+4)-5/(2y+8)=-1; or 12/(2y+8)-5/(2y+8)=-1. Further transformation yields:

7/(2y+8)=-1 or 7=-(2y+8)

7=-2y-8 or 2y=-7-8=-15; y=-15/2=-7.5.