Question

How do you solve `5/x + 6/x = 12`?

Answer 1

`x = 11/12`

Explanation:

Make sure that every term in the equation (including the total) has a common denominator.

12 as a fraction is `12/1`

So what we have is:
`5/x + 6/x = 12/1`

We need to find the LCD (least common denominator), which in this case would be `x`. Both `5/x` and `6/x` have the common denominator of `x` but `12/1` doesn't. To make sure that it does have the common denominator of `x`, we need to multiply both the denominator and the numerator by `x` (`{12 times x}/{1 times x} = (12x)/x`).

Now we have:
`5/x + 6/x = (12x)/x`

Since all of the terms have a common denominator, we can just simply evaluate for what `x` is equal to.
`5 + 6 = 12x`
`11 = 12x`
`11/12 = x`