Question

Solve x/x+1 + x+1/x = 34/15

Answer 1

Ans.

$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{34}{15} \\ or \: \frac{ {x}^{2} + {x}^{2} + 2x + 1 }{x(x + 1)} = \frac{34}{15} \\ or \: \frac{2 {x}^{2} + 2x + 1 }{ {x}^{2} + x } = \frac{34}{15} \\ or \: 30 {x}^{2} + 30x + 15 = 34 {x}^{2} + 34x \\ or \: 4 {x}^{2} + 4x - 15 = 0 \\ or \: (2x - 3)(2x + 5) = 0$

Therefore the required solution be
$x = \frac{3}{2} \: \: \: and \: \: \: x = - \frac{5}{2}$

I HOPE THAT THIS HELPS YOU.

Answer 2

x2+(x+1)^2/x(x+1)=34/15
30x^2+30x+15=34x^2+34x
-4x+15=4x^2
4x^2+4x-15=0
4x^2+10x-6x-15=0
2x(2x+5)-3(2x+5)
(2x+5)(2x-3)
x=-5/2 and 3/2

HOPE IT HELPS
PLEASE MARK IT AS BRAINLIEST