SOLUTION: Please Solve 1/x - 1/x+4 = 1/3

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Question 908849: Please Solve 1/x - 1/x+4 = 1/3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if you have:
1%2Fx+-+1%2Fx%2B4+=+1%2F3
cross%281%2Fx+%29-+cross%281%2Fx%29%2B4+=+1%2F3
4+=+1%2F3 ...since 4+%3C%3E+1%2F3, there is no solution

but, if you have:
+1%2Fx+-+1%2F%28x%2B4%29+=+1%2F3+ , than find common denominator

1%28x%2B4%29%2F%28x%28x%2B4%29%29+-+1%2Ax%2F%28x%28x%2B4%29%29+=+1%2F3

%28%28x%2B4%29-+x%29%2F%28x%28x%2B4%29%29+=+1%2F3
+4%2F%28x%28x%2B4%29%29+=+1%2F3....cross multiply
4%2A3+=+1%2A%28x%28x%2B4%29%29
12+=+x%5E2%2B4x
0+=+x%5E2%2B4x-12 or
x%5E2%2B4x-12=0 ...solve for x by factoring; write 4x as 6x-2x
+x%5E2%2B6x-2x-12+=+0+ ...group
+%28x%5E2%2B6x%29-%282x%2B12%29+=+0+
+x%28x%2B6%29-2%28x%2B6%29+=+0+
+%28x-2%29%28x%2B6%29+=+0+

solutions:
if +x-2+=+0+ => x=2
if +x%2B6+=+0+ => x=-6