First, multiply each side of the equation by #color(red)(y - 8)# to eliminate the fractions while keeping the equation balanced:
#color(red)(y - 8) xx (y - 7)/(y - 8) = color(red)(y - 8) xx 1/(y - 8)#
#cancel(color(red)(y - 8)) xx (y - 7)/color(red)(cancel(color(black)(y - 8))) = cancel(color(red)(y - 8)) xx 1/color(red)(cancel(color(black)(y - 8)))#
#y - 7 = 1#
Next, add #color(red)(7)# to each side of the equation to solve for #y# while keeping the equation balanced:
#y - 7 + color(red)(7) = 1 + color(red)(7)#
#y - 0 = 8#
#y = 8#
However, this solution is excluded because: #(8 - 8) = 0# in each of the denominators which means we would be dividing by #0# which is not allowed.
Therefore, there is no solution to this equation. Or, the solution is the null or empty set: #{O/}#
