SOLUTION: Solve for "u" 1/u + 5/u-2 = 4/u-2 So far I know I have to find a common denominator so I multiply by "u" or "u-2" and I have 1(u-2)/u(u-2) + 5u/u(u-2)=4u/u(u-2) but then I e

Algebra ->  Expressions-with-variables -> SOLUTION: Solve for "u" 1/u + 5/u-2 = 4/u-2 So far I know I have to find a common denominator so I multiply by "u" or "u-2" and I have 1(u-2)/u(u-2) + 5u/u(u-2)=4u/u(u-2) but then I e      Log On


   

Question 152604: Solve for "u"
1/u + 5/u-2 = 4/u-2
So far I know I have to find a common denominator so I multiply by "u" or "u-2" and I have 1(u-2)/u(u-2) + 5u/u(u-2)=4u/u(u-2) but then I end up with a bunch of u^2 and I am not sure what to do.
Thanks so much
Found 3 solutions by Earlsdon, jim_thompson5910, Edwin McCravy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for u:
1%2Fu+%2B+5%2F%28u-2%29+=+4%2F%28u-2%29 The LCD is u(u-2), so...
%28%28u-2%29%2B5u%29%2F%28u%28u-2%29%29+=+4u%2F%28u%28u-2%29%29 Multiplying through by u(u-2), we get:
%28u-2%29%2B5u+=+4u Combine like terms.
6u-2+=+4u Subtract 4u from both sides.
2u-2+=+0 Add 2 to both sides.
2u+=+2 Finally, divide both sides by 2.
u+=+1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%29%2F%28u%29%2B%285%29%2F%28u-2%29=%284%29%2F%28u-2%29 Start with the given equation.


%281%29%2F%281u%29%2B%285%29%2F%28u-2%29=%284%29%2F%28u-2%29 Factor any denominators.


Multiply every term on both sides by the LCD u%28u-2%29. Doing this will eliminate all of the fractions.


u-2%2B5u=4u Simplify


6u-2=4u Combine like terms on the left side.


6u=4u%2B2 Add 2 to both sides.


6u-4u=2 Subtract 4u from both sides.


2u=2 Combine like terms on the left side.


u=%282%29%2F%282%29 Divide both sides by 2 to isolate u.


u=1 Reduce.


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Answer:

So the answer is u=1

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


1%2Fu+%2B+5%2F%28u-2%29+=+4%2F%28u-2%29

Put parentheses around all the terms:

%281%2Fu%29+%2B+%285%2F%28u-2%29%29+=+%284%2F%28u-2%29%29

The LCD is u%2A%28u-2%29.  Put that over 1
like this u%2A%28u-2%29%2F1. Put parentheses
around it like this %28u%2A%28u-2%29%2F1%29.

Multiply every term by it:



Cancel whatever will cancel:



All that's left is

%28u-2%29%2B5u=4u

u-2%2B5u=4u

6u-2=4u

6u=4u%2B2

2u=2

u=1

This does not cause any denominators
to become 0 in the original, so it
is the solution.

Edwin