Question

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

Answer 1

Answer:

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

5x+5+4x=2

5x+4x=2-5

x=-3

Answer 2

Answer:

x = [5 ± √(105)](1/8)

Step-by-step explanation:

We are given that

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

Multiplying by 2x(x+1) on both sides we get

   4x + 5(x+1) = 4x(x+1)

  4x + 5x + 5 = 4x² + 4x

Subtracting 4x on both sides we get

          5x + 5 = 4x²

⇒ 4x² - 5x - 5 = 0

If we comparing it by ax² +bx +c = 0 we get

a = 4   ,   b = -5   , c = -5

BY using quadratic formula

x = [-b ± √(b² - 4ac)](1/2a)

Putting values we get

x = [5 ± √(25 + 80)](1/8)

x = [5 ± √(105)](1/8)

SO either

x =  [5 + √(105)](1/8)

or

x =  [5 - √(105)](1/8).