document.write( "Question 756620: Please help me solve for t!!!!\r
\n" ); document.write( "\n" ); document.write( "7t/a-t - a+t/7t \n" ); document.write( "
Algebra.Com's Answer #460382 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
We cannot solve for t from what was posted.
\n" ); document.write( "There is no equal sign, so there is no equation that would give any information about t.
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\n" ); document.write( "EXAMPLES:
\n" ); document.write( "7t/(a-t) = (a+t)/7t and 7t/a-t = a+t/7t
\n" ); document.write( "are equations because each one has an equal sign.
\n" ); document.write( "They can be solved for t, and I will show you how I would solve them.
\n" ); document.write( "NOTE:
\n" ); document.write( "Those parentheses make a big difference in the meaning of the expressions on both sides of the equal sign.
\n" ); document.write( "With pencil and paper, I can easily write
\n" ); document.write( "7t/(a-t) = (a+t)/7t as \"7t%2F%28a-t%29+=+%28a%2Bt%29%2F7t\".
\n" ); document.write( "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.
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\n" ); document.write( "7t/a-t = a+t/7t can be written as \"7t%2Fa-t+=+a%2Bt%2F7t\"
\n" ); document.write( "which can be simplified to \"7t%2Fa-t+=+a%2B1%2F7\"
\n" ); document.write( "I don't like equations with fractions, so at this time, I would multiply everything times 7. That gives me the equivalent equation
\n" ); document.write( "\"49t%2Fa-7t+=+7a%2B1\"
\n" ); document.write( "Taking out common factor t, we get
\n" ); document.write( "\"%2849%2Fa-7%29t+=+7a%2B1\" --> \"%2849%2Fa-7a%2Fa%29t+=+7a%2B1\" --> \"%28%2849-7a%29%2Fa%29t+=+7a%2B1\"
\n" ); document.write( "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\"
\n" ); document.write( "\"%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\"
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\n" ); document.write( "7t/(a-t) = (a+t)/7t can be written as \"7t%2F%28a-t%29+=+%28a%2Bt%29%2F7t\"
\n" ); document.write( "Multiplying oth sides of the equal sign times \"7t\" we get
\n" ); document.write( "\"49t%5E2%2F%28a-t%29+=+%28a%2Bt%297t%2F7t\" --> \"49t%5E2%2F%28a-t%29=a%2Bt\"
\n" ); document.write( "Next, multiplying oth sides of the equal sign times \"%28a-t%29\" we get
\n" ); document.write( "\"49t%5E2%28a-t%29%2F%28a-t%29=%28a%2Bt%29%28a-t%29\" --> \"49t%5E2=a%5E2-t%5E2\"
\n" ); document.write( "Now, adding \"t%5E2\" to both sides of the equation, we get
\n" ); document.write( "\"50t%5E2=a%5E2\" --> \"t%5E2=a%5E2%2F50\"
\n" ); document.write( "There are two solutions to that equation.
\n" ); document.write( "One is \"t=a%2Fsqrt%2850%29\" and it can be written more elegantlu as \"t=a%2Asqrt%282%29%2F5\".
\n" ); document.write( "The other solution is \"t=-a%2Fsqrt%2850%29\" , which can be written more elegantly as \"t=-a%2Asqrt%282%29%2F5\".\r
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