SOLUTION: 1/(x-3)+ 7 = x/(x-3) solve for x The answer is 10/3, how are they getting there????

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Question 23695: 1/(x-3)+ 7 = x/(x-3) solve for x
The answer is 10/3, how are they getting there????
Found 2 solutions by Earlsdon, rapaljer:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
1%2F%28x-3%29+%2B+7+=+x%2F%28x-3%29 Add the terms on the left side. Common denominator is (x-3)
%281+%2B+7%28x-3%29%29%2F%28x-3%29+=+x%2F%28x-3%29 Multiply both sides by (x-3) and simplify.
1%2B7x-21+=+x Subtract x from both sides.
1%2B6x+-21+=+0 Simplify the left side.
6x-20+=+0 Add 20 to both sides.
6x+=+20 Divide both sides by 6.
x+=+20%2F6 Simplify.
x+=+10%2F3

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply both sides of the equation by the LCD which is (x-3)

1%2F%28x-3%29%2B+7+=+x%2F%28x-3%29
%28x-3%29%2A%281%2F%28x-3%29%29%2B+7%2A%28x-3%29++=%28x-3%29%2A%28+x%2F%28x-3%29%29

The x-3 divides out in the first and last fractions leaving :

1+%2B+7%28x-3%29+=+x
1%2B7x+-21+=+x
7x+-+20+=+x

Add +20 to each side:
7x+-20%2B+20+=+x%2B+20
7x=++x%2B20

Now, subtract x from each side:
7x+-+x+=+x%2B20+-x
6x=+20

Divide by 6:
%286x%29%2Fx+=+20%2F6

Reduce the fraction:
x+=+10%2F3

Check to make sure no denominators are zero. The answer is acceptable.

R^2 at SCC