Question

Question #86fb5

Answer 1

`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.