SOLUTION: how do i solve b over b-2 plus 2 over 3 equals 2 over b-2

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Question 145676: how do i solve b over b-2 plus 2 over 3 equals 2 over b-2
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
b%2F%28b-2%29+%2B+2%2F3+=+2%2F%28b-2%29 Combine the fractions on the left. The LCD is 3(b-2)
%283b%2B2%28b-2%29%29%2F3%28b-2%29+=+2%2F%28b-2%29 Multiply both sides by 3.
%283b%2B2b-4%29%29%2F%28b-2%29+=+6%2F%28b-2%29 Simplify the left side.
%285b-4%29%2F%28b-2%29+=+6%2F%28b-2%29 Since the denominators of both sides are equal, the numerators are also equal, so...
5b-4+=+6 Add 4 to both sides.
5b+=+10 Divide both sides by 5.
b+=2
Now, if you try to check the solution, you will see that you get an undefined quantity.
b%2F%28b-2%29+%2B+2%2F3+=+2%2F%28b-2%29 Substitute b = 2.
2%2F%282-2%29+%2B+2%2F3+=+2%2F%282-2%29
2%2F0+%2B+2%2F3+=+2%2F0 ...and, as you know, in math division by zero is not allowed, so you have an undefined or indeterminate solution.