How do you solve $2/(x-1) - 2/3 =4/(x+1)$ ?

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Answer 1 · 2017-03-31T09:05:43

$x = -5 or 2$

$2/(x-1) - 2/3 = 4/(x+1)$

$=>$ $2/(x-1)-4/(x+1)=2/3$

$implies$ $(2(x+1)-4(x-1))/((x-1)*(x+1)) = 2/3$

$implies$ $(2(x+1)-4(x-1))/(x^2-1) = 2/3$

$implies$ $(6-2x)3 = 2(x^2-1)$
$implies$ $(3-x)3=x^2-1$
$implies$ $x^2+3x-10=0$

[ solution of a general quadratic equation of the form $ax^2+bx+c=0$ is given by
$x=(-b+-sqrt(b^2-4ac))/(2a)$ ]

$implies$ $x= (-3+-sqrt(9+40))/2$
$implies$ $x = (-3+-7)/2$
$implies$ $x = -5, 2$

How do you solve 2/(x-1) - 2/3 =4/(x+1)2/(x-1) - 2/3 =4/(x+1)?