SOLUTION: Please solve: Let g(x) = {{{ x/(4 - 2x) }}} Find {{{ (g(t) - g(1))/(t - 1) }}} and simplify

Algebra ->  Permutations -> SOLUTION: Please solve: Let g(x) = {{{ x/(4 - 2x) }}} Find {{{ (g(t) - g(1))/(t - 1) }}} and simplify       Log On


   

Question 906737: Please solve:

Let g(x) = ++x%2F%284++++-++++2x%29++ Find ++%28g%28t%29++++-++++g%281%29%29%2F%28t+-+1%29++ and simplify



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29+=+x%2F%284-2x%29

g%28t%29+=+t%2F%284-2t%29

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g%28x%29+=+x%2F%284-2x%29

g%281%29+=+1%2F%284-2%281%29%29

g%281%29+=+1%2F2

-------------------------------------------------------

%28g%28t%29-g%281%29%29%2F%28t-1%29+=+%28t%2F%284-2t%29+-+1%2F2%29%2F%28t-1%29

%28g%28t%29-g%281%29%29%2F%28t-1%29+=+%282t%2F%282%284-2t%29%29+-+1%2F2%29%2F%28t-1%29







%28g%28t%29-g%281%29%29%2F%28t-1%29+=+%28%284t+-+4%29%2F%282%284-2t%29%29%29%2F%28t-1%29



%28g%28t%29-g%281%29%29%2F%28t-1%29+=+%284t+-+4%29%2F%282%28t-1%29%284-2t%29%29

%28g%28t%29-g%281%29%29%2F%28t-1%29+=+%284%28t+-+1%29%29%2F%282%28t-1%29%284-2t%29%29





%28g%28t%29-g%281%29%29%2F%28t-1%29+=+4%2F%282%284-2t%29%29

%28g%28t%29-g%281%29%29%2F%28t-1%29+=+4%2F%28-4t+%2B+8%29

%28g%28t%29-g%281%29%29%2F%28t-1%29+=+4%2F%28-4%2A%28t+-+2%29%29

%28g%28t%29-g%281%29%29%2F%28t-1%29+=+-1%2F%28t-2%29

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So, %28t%2F%284-2t%29+-+1%2F2%29%2F%28t-1%29 simplifies to -1%2F%28t-2%29


In the end, %28g%28t%29-g%281%29%29%2F%28t-1%29+=+-1%2F%28t-2%29