Solve the rational equation 5 over 2x, minus 3 over x, equal to one quarter.

1. The three denominators are 2x, x and 4, so the least common denominator is 4x. 2. The value 0 must be excluded from the start, since it makes two denominators vanish. 3. Multiply every term by 4x so that no denominators are left. 4. The first term becomes 4x times 5 over 2x, which is 10. 5. The second term becomes 4x times 3 over x, which is 12. 6. The right side becomes 4x times one quarter, which is x. 7. So the equation reads 10 minus 12 equal to x, giving x equal to negative 2. 8. The answer x = 2 drops the minus sign when subtracting 12 from 10. 9. The answers x = -8 and x = 8 come from using 2x rather than 4x as the common denominator. _Source: OpenStax College Algebra (CC BY 4.0), section 2.2 Linear Equations in One Variable_