Question

How do you solve `(3x+6)/(x^2-4)=(x+1)/(x-2)`?

Answer 1

`x =2`

Explanation:

Well there is the long way. Cross multiply
`(3x+6)(x-2)=(x^2-4)(x +1)`
Multiply out solve

Or there is the efficient way. Factorise each term first.
`[3(x +2)]/[(x+2)(x-2)]=(x +1)/(x-2)`

Cancel and we are left with 3=`x`+1

Answer 2

This equation has no solution.

Explanation:

`((3(x + 2))/((x + 2)(x - 2)))/((x + 1)/(x - 2)) = 1`

`(3(x + 2)(x - 2))/((x + 2)(x - 2)(x + 1)) = 1`

Cancelling using the property `a/a = 1`, we are left with:

`3/(x + 1) = 1`

`3 = 1(x + 1)`

`3 = x + 1`

`x = 2`

However, this value of `x` is extraneous, since it renders the denominator `0` (which in turn makes the equation undefined).

Hence, this equation has no solution `{O/}`.

Hopefully this helps!