How do I solve fractions with unknowns in the denominators?
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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
