Question 695496
{{{ (a-t)/(b-t) = c }}}
First multiply by (b-t) to remove the denominator:
{{{ (a-t) = c(b-t) }}}
Next multiply out:
{{{ a-t = cb - ct }}}
Collect term on t on the LHS:
{{{ -t + ct = cb - a }}}
Factorise out the t term:
{{{ t(c-1) = cb - a }}}
and divide by non-t terms:
{{{ t = (cb - a)/(c-1) }}}