Question

Roots of equation (x/(x-1)) + ((x-1)/x) = 13/6 are?

Answer 1

Answer:

Step-by-step explanation:

$\frac{x}{x-1}+\frac{x-1}{x}=\frac{13}{6}\\\\let \;\;\frac{x}{x-1}=y\\\\y+\frac{1}{y}=\frac{13}{6}\\\\6y^2-13y+6=0\\\\6y^2-9y-4y+6=0\\\\3y(2y-3)-2(2y-3)=0\\\\(3y-2)(2y-3)=0\\\\y=\frac{3}{2}\\\\y=\frac{2}{3}\\\\If y=\frac{3}{2}\\\\\frac{3}{2}=\frac{x}{x-1}\\\\3x-3=2x\\\\x=3\\\\if\;\;y=\frac{2}{3}\\\\\frac{2}{3}=\frac{x}{x-1}\\\\2x-2=3x\\\\x=2\\\\Therefore\;x=2\;and\;x=3\;are \;roots\;of\;the\;eqn$

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