riding once again
Join Date: Oct 2005
Location: San Diego, CA
Bikes: '06 Cervelo R3, '05 Specialized Allez
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Suppose (x+1)/(x-1) = (x+2)/(x-2) is our problem.
Upon inspection, there's no obvious tricks, so we'll take the most common strategy (and the only one in this case that is particularly helpful) of multiplying by the two denominators.
Multiply both sides by (x-1) * (x-2), and you get (x+1)*(x-2) = (x+2)*(x-1), or
x^2 - x - 2 = x^2 + x - 2.
In this trivial case, you get -x = x, or x = 0. We double check our solution, and indeed, x = 0 satisfies the original equation. In a more general case, once you get to something like the above, it's a simple problem in algebra (in the general case to be solved by making one side equal to zero, then either factoring or falling back on the quadratic equation).
Hope that helps. Feel free to post or PM me with an attempt at one of the problems you mentioned if you want to see if you're doing everything right.
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