Question

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

Answer 1

Roots are real ; `x= 1.317 , x= -5.317 (3dp)`

Explanation:

`3/(x^2-4) = (2(x-2)+x(x+2))/(x^2-4)`or `2x-4+x^2+2x-3=0 or x^2+4x-7=0`This is a quadratic equation of form `ax^2+bx+c; a=1 ; b=4; c=-7`
roots are real as `b^2-4ac` is positive. Roots are `-b/(2a)+- sqrt (b^2-4ac)/(2a) = -4/2+-sqrt44/2 = 1.317, -5.317`[Ans]