How do I solve fractions with unknowns in the denominators?

To solve the equation: (5x+3)/(x) + x = 1, where (x) is the denominator, we have to convert the equation into an equation without any denominators.

To do this, we multiply each variable by (x), so the equation becomes: (5x+3) + (x)(x) = (1)(x).

The next step is to expand the brackets: 5x + 3 + x^2  = x

After this, we move all variables onto one side of the equation (by subtracting x from both sides) so that it equals 0: x^2 + 4x + 3 = 0 

Factorsing this equation we get: (x + 3)(x + 1) = 0

Therefore, we can equate each bracket to 0, giving the solutions for x:

x + 3 = 0, x = -3

x + 1 = 0, x = -1