# How do you solve the rational equation #x+3/(2x) = 5/8#?

Simplify then use the quadratic formula

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To solve the rational equation x + 3/(2x) = 5/8, you can follow these steps:

- Multiply both sides of the equation by the common denominator, which is 8x. This will eliminate the fractions.

8x(x) + 8x(3/(2x)) = 8x(5/8)

- Simplify the equation by distributing and canceling out common factors.

8x^2 + 12 = 5x

- Rearrange the equation to bring all terms to one side, setting it equal to zero.

8x^2 - 5x + 12 = 0

- This quadratic equation cannot be factored easily, so you can use the quadratic formula to find the solutions.

The quadratic formula is x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 8, b = -5, and c = 12.

x = (-(-5) ± √((-5)^2 - 4(8)(12)))/(2(8))

- Simplify the equation under the square root.

x = (5 ± √(25 - 384))/(16)

x = (5 ± √(-359))/(16)

- Since the square root of a negative number is not a real number, this equation has no real solutions.

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