First, mutliply each side of the equation by the lowest common denominator of the fractions, #color(blue)(4)color(red)((w - 6))# to eliminate the fractions while keeping the equation balanced:
#color(blue)(4)color(red)((w - 6)) xx (w + 5)/(w - 6) = color(blue)(4)color(red)((w - 6)) xx 5/4#
#color(blue)(4)cancel(color(red)((w - 6))) xx (w + 5)/color(red)(cancel(color(black)(w - 6))) = cancel(color(blue)(4))color(red)((w - 6)) xx 5/color(blue)(cancel(color(black)(4)))#
#4(w + 5) = 5(w - 6)#
Next, expand the terms within parenthesis by multiplying them by the term outside the parenthesis:
#(4 xx w) + (4 xx 5) = (5 xx w) - (5 xx 6)#
#4w + 20 = 5w - 30#
Then, subtract #color(red)(4w)# and add #color(blue)(30)# to each side of the equation to solve for #w# while keeping the equation balanced:
#4w + 20 - color(red)(4w) + color(blue)(30) = 5w - 30 - color(red)(4w) + color(blue)(30)#
#4w - color(red)(4w) + 20 + color(blue)(30) = 5w - color(red)(4w) - 30 + color(blue)(30)#
#0 + 50 = (5 - color(red)(4))w - 0#
#50 = 1w#
#50 = w#
#w = 50#
