SOLUTION: This actually has to do with radical equations, but can you please explain how you'd solve the equation 1 over t-2 = t over 8. I think you can read that better, but its 1/t-2 = t/

Algebra ->  Equations -> SOLUTION: This actually has to do with radical equations, but can you please explain how you'd solve the equation 1 over t-2 = t over 8. I think you can read that better, but its 1/t-2 = t/      Log On


   

Question 309231: This actually has to do with radical equations, but can you please explain how you'd solve the equation 1 over t-2 = t over 8.
I think you can read that better, but its 1/t-2 = t/8, and I'm supposed to solve for t.
Thank for your very valuable time.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I think you meant to say rational equations. Radical equations look something like this sqrt%28x%29=10. Also, you can use parenthesis to show that 't-2' is underneath 1 by typing 1/(t-2)


1%2F%28t-2%29+=+t%2F8 Start with the given equation.


1%2A8+=+t%28t-2%29 Cross multiply


1%2A8+=+t%2At-t%2A2 Distribute


8+=+t%5E2-2t Multiply


0+=+t%5E2-2t-8 Subtract 8 from both sides.


Notice that the quadratic t%5E2-2t-8 is in the form of At%5E2%2BBt%2BC where A=1, B=-2, and C=-8


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-8


t+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


t+=+%282+%2B-+sqrt%28+4-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


t+=+%282+%2B-+sqrt%28+4--32+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-8%29 to get -32


t+=+%282+%2B-+sqrt%28+4%2B32+%29%29%2F%282%281%29%29 Rewrite sqrt%284--32%29 as sqrt%284%2B32%29


t+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%281%29%29 Add 4 to 32 to get 36


t+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


t+=+%282+%2B-+6%29%2F%282%29 Take the square root of 36 to get 6.


t+=+%282+%2B+6%29%2F%282%29 or t+=+%282+-+6%29%2F%282%29 Break up the expression.


t+=+%288%29%2F%282%29 or t+=++%28-4%29%2F%282%29 Combine like terms.


t+=+4 or t+=+-2 Simplify.


So the solutions are t+=+4 or t+=+-2