Question

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

Answer 1

`x=-1/2+sqrt(105)/5color(white)("xxx")"or"color(white)("xxx")x=-1/2-sqrt(105)/6`

Explanation:

Given
`color(white)("XXX")2/(x+1)=(3x)/4`

`rArr`
`color(white)("XXX")2xx4=(3x) xx (x+1)`

`color(white)("XXX")8=3x^2+3x`

`color(white)("XXX")3x^2+3x-8=0`

(applying the quadratic formula)
`color(white)("XXX")x=(-3+-sqrt(3^2-4 * 3 * (-8)))/(2 * 3)`

`color(white)("XXXx")=(-3+-sqrt(9+96))/6`

`color(white)("XXXx")=-1/2+-sqrt(105)/6`