8/x - 3/(x+1) = 5

8 - 3x/(x + 1) = 5x Multiply both sides by x

8(x + 1) - 3x = 5x(x + 1) Muliply both sides by (x + 1)

8x + 8 - 3x = 5x^2 + 5x Expand the parenthesis

5x + 8 = 5x^2 + 5x Simplify

8 = 5x^2 Subtract 5x from both sides

8/5 = x^2 Divide both sides by 5

+- 2*sqrt(2/5) = x Take the square root

(8/x)-(3/(x+1)) = 5.

The denominators are x and x+1 . So we multiply by the LCM of the deenominators, x(x+1) both sides to get rid of the denominators:

8(x+1) -3(x)= 5x(x+1)

Simplify both sides:

8x+8-3x = 5x^2+5x

5x+8=5x^2+5x

Divide both sides by 5.

subtract 5x from both sides:

8=5x^2

8/5=x^2

Take square root on both sides:

x= **+sqrt(8/5) ** = **1.264911064** or

x= **-sqrt(8/5) =-1.264911064**

(8/x) - {3/(x+1)} = 5

8/x - 3/x+1 = 5

Find the LCM which in this case is x(x+1)

8(x+1)/x(x+1) - 3x/x(x+1) = 5

8x+8-3x/x(x+1) = 5

5x+8/x(x+1) = 5

5x+8/x^2 + x = 5

5x + 8 = 5x^2 + 5x

8 = 5x^2 + 5x - 5x

8 = 5x^2

8/5 = x^2

sqrt(8/5) = sqrt(x^2) Take square root on both sides

sqrt8/5 = x

therefore,

x = + sqrt(8/5)

x = - sqrt(8/5)