SOLUTION: how can i show work on this question? 5/x+2/5=7/x

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Question 897709: how can i show work on this question?
5/x+2/5=7/x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here is one way to solve for x. First I combined the fractions on the left side (by getting the LCD first). From there I cross multiplied and then isolated x.

5%2Fx%2B2%2F5=7%2Fx

%285%2A5%29%2F%285%2Ax%29%2B2%2F5=7%2Fx

25%2F%285x%29%2B2%2F5=7%2Fx

25%2F%285x%29%2B%28x%2A2%29%2F%28x%2A5%29=7%2Fx

25%2F%285x%29%2B%282x%29%2F%285x%29=7%2Fx

%2825%2B2x%29%2F%285x%29=7%2Fx

%2825%2B2x%29%2Ax=5x%2A7

x%2825%2B2x%29=5x%2A7

x%2825%29%2Bx%282x%29=5x%2A7

25x%2B2x%5E2=35x

25x%2B2x%5E2-35x=0

2x%5E2%2B25x-35x=0

2x%5E2-10x=0

2x%28x-5%29=0

2x=0 or x-5=0

x=0%2F2 or x-5=0

x=0 or x-5=0

x=0 or x=0%2B5

x=0 or x=5

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The two *possible* solutions are x=0 or x=5

However, only x=5 works because plugging x=0 back into the original equation gives you a division by zero error.

So the final answer is x+=+5