Find The Solution For Rational Equation (2/(X+1)+5/2x)=2

Find the solution for rational equation (2/(x+1)+5/2x)=2

 

Answer:

x = (5 ± √105 ) / 8

Step-by-step explanation:

find the solution for rational equation (2 / (x + 1) + 5 / 2x) = 2

multiply both sides by (x + 1) (2x)

2(2x) + 5(x + 1) = 2(x + 1)(2x)

4x + 5x + 5 = 4x² + 4x

combine like terms

4x² + 4x - 9x - 5 = 0

4x² - 5x - 5 = 0

a = 4

b = -5

c = -5

use quadratic formula

x = -b ± √(b² - 4ac) / 2a

x = 5 ± √((-5)² - 4(4)(-5)) / 2(4)

x = 5 ± √(25 + 80) / 8

x = (5 ± √105 ) / 8