Question #e806e

1 Answer
Aug 19, 2015

Answer:

#(2x-3)/(2x-5)#

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 #x# to get

#(color(red)(cancel(color(black)(x))) * (2x - 3))/(color(red)(cancel(color(black)(x))) * (2x - 5)) = color(green)((2x-3)/(2x-5))#