Question

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

Answer 1

Simplify then use the quadratic formula

Explanation:

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`