SOLUTION: Please help me solve for t!!!! 7t/a-t - a+t/7t

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Question 756620: Please help me solve for t!!!!
7t/a-t - a+t/7t

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We cannot solve for t from what was posted.
There is no equal sign, so there is no equation that would give any information about t.

EXAMPLES:
7t/(a-t) = (a+t)/7t and 7t/a-t = a+t/7t
are equations because each one has an equal sign.
They can be solved for t, and I will show you how I would solve them.
NOTE:
Those parentheses make a big difference in the meaning of the expressions on both sides of the equal sign.
With pencil and paper, I can easily write
7t/(a-t) = (a+t)/7t as 7t%2F%28a-t%29+=+%28a%2Bt%29%2F7t.
Those long horizontal fraction lines above a-t and below a%2Bt include invisible parentheses wrapping everything written above the line, and everything written below the line.

7t/a-t = a+t/7t can be written as 7t%2Fa-t+=+a%2Bt%2F7t
which can be simplified to 7t%2Fa-t+=+a%2B1%2F7
I don't like equations with fractions, so at this time, I would multiply everything times 7. That gives me the equivalent equation
49t%2Fa-7t+=+7a%2B1
Taking out common factor t, we get
%2849%2Fa-7%29t+=+7a%2B1 --> %2849%2Fa-7a%2Fa%29t+=+7a%2B1 --> %28%2849-7a%29%2Fa%29t+=+7a%2B1
Finally, we get the solution by multiplying both sides of the equal sign times a%2F%2849-7a%29, which is the same as dividing by %2849-7a%29%2Fa
%28%2849-7a%29%2Fa%29t=7a%2B1 --> %28%2849-7a%29%2Fa%29%28%2849-7a%29%2Fa%29t+=+%28%2849-7a%29%2Fa%297a%2B1 --> t=%287a%2B1%29%2849-7a%29%2Fa --> t=%28343a-49a%5E2%2B49-7a%29%2Fa --> t=%2849%2B336a-49a%5E2%29%2Fa

7t/(a-t) = (a+t)/7t can be written as 7t%2F%28a-t%29+=+%28a%2Bt%29%2F7t
Multiplying oth sides of the equal sign times 7t we get
49t%5E2%2F%28a-t%29+=+%28a%2Bt%297t%2F7t --> 49t%5E2%2F%28a-t%29=a%2Bt
Next, multiplying oth sides of the equal sign times %28a-t%29 we get
49t%5E2%28a-t%29%2F%28a-t%29=%28a%2Bt%29%28a-t%29 --> 49t%5E2=a%5E2-t%5E2
Now, adding t%5E2 to both sides of the equation, we get
50t%5E2=a%5E2 --> t%5E2=a%5E2%2F50
There are two solutions to that equation.
One is t=a%2Fsqrt%2850%29 and it can be written more elegantlu as t=a%2Asqrt%282%29%2F5.
The other solution is t=-a%2Fsqrt%2850%29 , which can be written more elegantly as t=-a%2Asqrt%282%29%2F5.