SOLUTION: 4/(y+2) = 1 - 8/(y(y+2)) I know the answer is 4 for this rational equation but I don't know how to solve it. An explanation would be very appreciated, thanks.

Algebra ->  Trigonometry-basics -> SOLUTION: 4/(y+2) = 1 - 8/(y(y+2)) I know the answer is 4 for this rational equation but I don't know how to solve it. An explanation would be very appreciated, thanks.       Log On


   

Question 917599: 4/(y+2) = 1 - 8/(y(y+2)) I know the answer is 4 for this rational equation but I don't know how to solve it. An explanation would be very appreciated, thanks.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F%28y%2B2%29+=+1+-+8%2F%28y%28y%2B2%29%29+
4+=+%281+-+8%2F%28y%28y%2B2%29%29%29%28y%2B2%29+
4+=+1%28y%2B2%29+-+%288%2F%28y%28y%2B2%29%29%29%28y%2B2%29+
4+=+1%28y%2B2%29+-+%288%2F%28y%2Across%28%28y%2B2%29%29%29%29cross%28%28y%2B2%29%29+
4+=+y%2B2+-+8%2Fy+
4-2+=+y+-+8%2Fy+
2+=+%28y%5E2+-+8%29%2Fy+
2y+=+y%5E2+-+8+
0+=+y%5E2+-2y-8+
+y%5E2+-4y%2B2y-8+=0
+%28y%5E2+-4y%29%2B%282y-8%29+=0
+y%28y+-4%29%2B2%28y-4%29+=0
%28y%2B2%29%28y-4%29=0
solutions:
if y%2B2=0 =>y=-2
if y-4=0=>y=4