Question #86fb5

1 Answer
Jan 17, 2018

#x = 2/3#

Explanation:

The formatting is kind of unclear, but I'm assuming the equation is:
#1/2 - 3/(x+3) = 5/(2(x+3)) - 1#

First, we will add one to both sides to simplify it:
#1 + 1/2 - 3/(x+3) = 5/(2(x+3))#.
Notice that #1 + 1/2 = 3/2# and that we can add #3/(x+3)# to both sides:
#3/2 = 5/(2(x+3)) + 3/(x+3)#.

Focusing on the side with the variable #x#, we can cross-multiply in order to get one common denominator and therefore, we can add the numerators:
#[5/(2(x+3)) * (x+3)/(x+3)] + [3/(x+3) * (2(x+3))/(2(x+3))]#
Proceeding with the multiplication, i.e. distributing everything, we will get:
#(5(x+3))/(2(x+3)^2) + (6(x+3))/(2(x+3)^2)#.

Notice that both the numerator and denominator share a #(x+3)# so we can simply cancel them out and get:
#3/2 = (5+6)/(2(x+3))#.

If we proceed via multiplying both sides by two, to get rid of the twos in the denominators, we will get #3 = 11/(x+3)#.

Then we multiply both sides by #(x+3)# so we can have our unknown in the numerator: #3(x+3) = 11# which is equivalent to #3x + 9 = 11#.

Proceed with simple algebra, and we will get that #x = 2/3#.

Checking this, we can see it is the answer.