Question #e806e

1 Answer
Aug 19, 2015

(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))