Question

solve for x plz do in rough nb

Answer 1

$\frac{x}{x-1} + \frac{x-1}{x} = 4 \\\\ \frac{x(x) + (x-1)(x-1)}{x(x-1)} = 4 \\\\ \frac{ x^{2} + (x-1)^{2} }{ x^{2} - x} = 4 \\\\ x^{2} + x^{2} +1 - 2(x)(1) = 4( x^{2} - x) \\\\ 2 x^{2} + 1-2x = 4 x^{2} - 4x \\\\ 4 x^{2} -2 x^{2} = 1-2x+4x \\\\ 2x^{2} = 1 + 2x \\\\ 2 x^{2} -2x -1 = 0$

Compare with ax²+bx+c = 0
a = 2 , b = -2 , c = -1

b²-4ac = (-2)² - 4(2)(-1)
= 4 + 8
= 12

x = -b ± √b²-4ac/2a
= [-(-2) ± √12]/2(2)
= (2±2√3)/4
= 2(1±√3)/4
= (1±√3)/2

x = (1+√3)/2 (or) x = (1-√3)/2

Answer 2

Hope this helps.....