First, we need to get each fraction over the same denominator so we can work with them. In this case #10x# will be a common denominator. So we must multiple each fraction by the appropriate form of #1# to have a denominator of #10x#:
#((5x)/(5x) * x/2 - 10/10 * 2/x)/(x/x * (x-3)/10 - 10/10 * 1/x) ->#
#((5x^2)/(10x) - 20/(10x))/((x^2-3x)/(10x) - 10/(10x)) ->#
#((5x^2 - 20)/(10x))/((x^2-3x - 10)/(10x)) ->#
Now, we can use the rules for dividing fractions to get:
#(10x * (5x^2 - 20))/(10x * (x^2-3x - 10)) ->#
#(cancel(10x) * (5x^2 - 20))/(cancel(10x) * (x^2-3x - 10)) ->#
#(5x^2 - 20)/(x^2-3x - 10) ->#
Factoring the numerator and denominator gives:
#((5x - 10 )(x + 2 ))/((x - 5)(x + 2))#
#((5x - 10 )cancel((x + 2)))/((x - 5)cancel((x + 2)))#
#((5x - 10 ))/((x - 5))#
