Question

Hello, the question is in the picture :)

Answer 1

By cross multiplying the given equation, we have

`6x=(x-2)(x+8)`

By multiplying the right hand side, we get

`6x=x^2+6x-16`

Then, by subtracting 6x to both sides, we have

`0=x^2-16`

or equivalently,

`x^2-16=0`

Since the left hand side is a conjugate binomial, it can be expressed as

`x^2-16=(x+4)(x-4)`

Then, we have the equation

`(x+4)(x-4)=0`

Therefore, the values of x that make the equation true are x= 4 and x= -4