How do you simplify #(x+1)/x - x/(x+1)#?

Question

Isaiah Anthony · Accepted Answer

#(x+1)/x - x/(x+1) = 1/x+1/(x+1)#

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)#

Kennedy Adams · Answer

#(2x+1)/(x(x+1)# Find the lowest common factor which is #x(x+1)# #(x+1)/x = x/(x+1)# #((x+1)(x+1) - (x xx x))/(x(x+1))# #(x^2+x+x+1 - x^2)/(x(x+1)# #(cancel(x^2-x^2)+2x+1)/(x(x+1)# #(2x+1)/(x(x+1)#

Hazel Anglin · Answer

#(2x+1)/(x(x+1))# #"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))#

Kennedy Adams · Answer

undefined To simplify the expression (x+1)/x - x/(x+1), we need to find a common denominator. The common denominator is x(x+1).

Multiplying the first fraction (x+1)/x by (x+1)/(x+1), we get (x+1)^2/(x(x+1)).

Multiplying the second fraction x/(x+1) by x/x, we get x^2/(x(x+1)).

Now, we can subtract the two fractions: (x+1)^2/(x(x+1)) - x^2/(x(x+1)).

Combining the fractions, we have [(x+1)^2 - x^2]/(x(x+1)).

Expanding the numerator, we get (x^2 + 2x + 1 - x^2)/(x(x+1)).

Simplifying further, we have (2x + 1)/(x(x+1)).

Therefore, the simplified expression is (2x + 1)/(x(x+1)).