Question #e806e
1 Answer
Explanation:
Your starting expression looks like this
#(2x + x/(x-2))/(2x - x/(x-2))#
This can be rewritten as
#(2x + x/(x-2)) * 1/((2x - x/(x-2)))#
Find the common denominator for the two terms that are written in parantheses
#2x + x/(x-2) = (2x) * (x-2)/(x-2) + x/(x-2) = (2x(x-2) + x)/(x-2)#
and
#2x - x/(x-2) = (2x) * (x-2)/(x-2) - x/(x-2) = (2x(x-2) - x)/(x-2)#
Your expression will now be
#(2x(x-2) + x)/((x-2)) * 1/((2x(x-2)-x)/(x-2))#
which is equivalent to
#(2x(x-2) + x)/color(red)(cancel(color(black)((x-2)))) * color(red)(cancel(color(black)((x-2))))/(2x(x-2)-x)#
#(2x(x-2) + x)/(2x(x-2) - x)#
Expand the parantheses to g et
#(2x * x + 2x * (-2) + x)/(2x * x + 2x * (-2) - x)#
#(2x^2 - 4x + x)/(2x^2 - 4x - x) = (2x^2 - 3x)/(2x^2 -5x)#
You can simplify this further by dividing the numerator and denominator by
#(color(red)(cancel(color(black)(x))) * (2x - 3))/(color(red)(cancel(color(black)(x))) * (2x - 5)) = color(green)((2x-3)/(2x-5))#
