How do you simplify # (2)/(x) + (2)/(x-1) - (2)/(x-2)#?
1 Answer
Mar 12, 2017
Explanation:
Before adding/subtracting algebraic fractions we require them to have a
#color(blue)"common denominator"# Multiply numerator/denominator of
# 2/x" by "(x-1)(x-2)# Multiply numerator/denominator of
# 2/(x-1)" by "x(x-2)# Multiply numerator/denominator of
# 2/(x-2)" by "x(x-1)#
#• 2/xto(2(x-1)(x-2))/(x(x-1)(x-2))=(2x^2-6x+4)/(x(x-1)(x-2))#
#• 2/(x-1)to(2x(x-2))/(x(x-1)(x-2))=(2x^2-4x)/(x(x-1)(x-2)#
#• 2/(x-2)to(2x(x-1))/(x(x-1)(x-2))=(2x^2-2x)/(x(x-1)(x-2))# Now the fractions have a common denominator we can add/subtract the numerators leaving the denominator as it is.
Putting the 3 simplifications together.
#rArr(2x^2-6x+4+2x^2-4x-(2x^2-2x))/(x(x-1)(x-2)#
#=(2x^2-8x+4)/(x(x-1)(x-2))#
#=(2(x^2-4x+2))/(x(x-1)(x-2))#