Question

How do you solve `x+ 3= \frac { 15- x } { 2x }`?

Answer 1

`x=1 1/2` or `x=-5`

Explanation:

Given
`color(white)("XXX")x+3=(15-x)/(2x)`

Multiplying both sides by `2x`
`color(white)("XXX")2x^2+6x=15-x`

Re-arranging the terms as a standard quadratic:
`color(white)("XXX")2x^2+7x-15=0`

Factoring the left side
`color(white)("XXX")(2x-3)(x+5)=0`

Which implies
`color(white)("XXX"){:(2x-3=0," or ", x+5=0),(x=3/2,,x=-5):}`