I have been presented with the following equation:

According to the text, the solution is6. I have been unable to reach this answer.

Here is the method I've used:

The LCD of is .

I multiply each side of the equation by the LCD and get the following:

which is then simplified into

From there I try to factor the left side of the equation, but it turns out being prime after using the FOIL method.

Yet somehow my textbook lists the solution as6. What am I doing wrong?

I encounter the same situation in another similar equation who's solution set is supposed to be 2, 3 :

Again, I determine the LCD is and multiply each side by this.

simplified to

I once again try to factor, but just as before

The solution set is supposedly2, 3. Grrrr...