Question

x/x+1+x+1/x=36/15, x≠0 x≠-1 qudratic equation by factorisation method ​

Answer 1

$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{36}{15} \\ \\ \frac{x}{x + 1} + \frac{x + 1}{x} = \frac{12}{5} \\ \\ \frac{ {x}^{2} + {(x + 1)}^{2} }{x(x + 1)} = \frac{12}{5} \\ \\ 5(2 {x}^{2} + 2x + 1) = 12( {x}^{2} + x) \\ \\ 2 {x}^{2} + 2x - 5 = 0 \\ \\ 2 {x}^{2} + 2x = 5 \\ \\ 2( {x}^{2} + x + \frac{1}{4} ) - \frac{1}{2} = 5 \\ \\ {(x + \frac{1}{2} )}^{2} = \frac{11}{4} \\ \\ x = \frac{ - 1 + | \sqrt{11} |}{2} \\ \\ x = \frac{ - 1 + \sqrt{11} }{2} \\ \\ x = \frac{ - 1 - \sqrt{11} }{2}$

hope it helps.