Question

How do you solve `x+ \frac { 6 } { x } = 5`?

Answer 1

`x=2` and `x=3`

Explanation:

I would approach this problem by finding the common denominator on both sides of the equation then simplify the equation.

`x+6/x=5`

The common denominator (LCD) is `x`

`(x^2+6)/(1 cancel x)=(5x)/(1 cancel x)`

Simplify the `x`'s or use another method but you will see that you will end up simplifying the `x`

`x^2+6=5x`

`x^2-5x+6=0`

Here, too you can use any method you are comfortable with, as for me I always find the `Delta`

`Delta=b^2-4ac`, with `a=1`, `b=-5` and `c=6`

`Delta=(-5)^2-4(1)(6)=1=>sqrt Delta=+-1`

`x_1=(-b+sqrt Delta)/(2a)` and `x_2=(-b-sqrt Delta)/(2a)`

`x_1=(5+1)/(2)=3` and `x_2=(5-1)/(2)=2`

So, `x=2` and `x=3` is your solution.