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

Question

Isaiah Anthony · Accepted Answer

Simplify then use the quadratic formula

Get rid of all the denominators and then solve as a standard quadratic. #(x*(2x) +3)/(2x) = 5/8# #8(2x^2 +3) = 5*(2x)# #16x^2 +24 -10x = 0# Then use the quadratic formula to solve as this does not have simple factors. #x = (-b +- sqrt(b^2 - 4ac))/(2a)# #x= (-24 +- sqrt( 24^2 - 4*16*(-10)))/(2*16) = (-24 +- sqrt(576 +640))/ 32# #x approx. 0.34 or -1.84#

Genesis Allen · Answer

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

1. 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)

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

8x^2 + 12 = 5x

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

8x^2 - 5x + 12 = 0

4. 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))

5. Simplify the equation under the square root.

x = (5 ± √(25 - 384))/(16)

x = (5 ± √(-359))/(16)

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