How do you simplify #(x+1)/x - x/(x+1)#?
3 Answers
Explanation:
Find the lowest common factor which is
Explanation:
#"we require the fractions to have a "color(blue)"common denominator"#
#"to obtain this"#
#"multiply the numerator/denominator of "(x+1)/x#
#"by "(x+1)#
#"and multiply numerator/denominator of "x/(x+1)" by "x#
#=((x+1)(x+1))/(x(x+1))-x^2/(x(x+1))#
#"the fractions now have a common denominator so expand"#
#"and subtract the numerator leaving the denominator"#
#=(cancel(x^2)+2x+1cancel(-x^2))/(x(x+1))#
#=(2x+1)/(x(x+1))#
Explanation:
I am not sure what is meant by simplified here, but we can find:
#(x+1)/x - x/(x+1) = (x+1)/x-((x+1-1)/(x+1))#
#color(white)((x+1)/x - x/(x+1)) = (1+1/x)-(1-1/(x+1))#
#color(white)((x+1)/x - x/(x+1)) = 1/x+1/(x+1)#