Question 906737
{{{g(x) = x/(4-2x)}}}


{{{g(t) = t/(4-2t)}}}


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{{{g(x) = x/(4-2x)}}}


{{{g(1) = 1/(4-2(1))}}}


{{{g(1) = 1/2}}}


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{{{(g(t)-g(1))/(t-1) = (t/(4-2t) - 1/2)/(t-1)}}}


{{{(g(t)-g(1))/(t-1) = (2t/(2(4-2t)) - 1/2)/(t-1)}}}


{{{(g(t)-g(1))/(t-1) = (2t/(2(4-2t)) - (4-2t)/(2(4-2t)))/(t-1)}}}


{{{(g(t)-g(1))/(t-1) = ((2t - (4-2t))/(2(4-2t)))/(t-1)}}}


{{{(g(t)-g(1))/(t-1) = ((2t - 4+2t)/(2(4-2t)))/(t-1)}}}


{{{(g(t)-g(1))/(t-1) = ((4t - 4)/(2(4-2t)))/(t-1)}}}


{{{(g(t)-g(1))/(t-1) = ((4t - 4)/(2(4-2t)))*(1/(t-1))}}}


{{{(g(t)-g(1))/(t-1) = (4t - 4)/(2(t-1)(4-2t))}}}


{{{(g(t)-g(1))/(t-1) = (4(t - 1))/(2(t-1)(4-2t))}}}


{{{(g(t)-g(1))/(t-1) = (4*highlight((t - 1)))/(2*highlight((t - 1))(4-2t))}}}


{{{(g(t)-g(1))/(t-1) = (4*cross((t - 1)))/(2*cross((t - 1))(4-2t))}}}


{{{(g(t)-g(1))/(t-1) = 4/(2(4-2t))}}}


{{{(g(t)-g(1))/(t-1) = 4/(-4t + 8)}}}


{{{(g(t)-g(1))/(t-1) = 4/(-4*(t - 2))}}}


{{{(g(t)-g(1))/(t-1) = -1/(t-2)}}}


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So, {{{(t/(4-2t) - 1/2)/(t-1)}}} simplifies to {{{-1/(t-2)}}}



In the end, {{{(g(t)-g(1))/(t-1) = -1/(t-2)}}}