1 1 5
----- + ----- = -
x - 1 x - 2 6
I multiplied each side by (x-1)(x-2)(6) to get rid of all the fractions, but once I do that, I get the following equation.
(x-2)(6) + (x-1)(6) = 5(x-1)(x-2)
From here, I'm stuck. No matter how I solve the eqution, x doesn't equate to 4, which is the correct answer (I found that out in my head). What am I missing here? I believe I did something wrong on the right side of the equation.
P_S
Working it out, here are my steps (I'm extremely rusty at this sort of thing, not having done it for nearly 5 years now, and I suspect that I'm taking the long way around, but it still works):
Well, since you said you suspected making a mistake on the right side of the equation, I'll walk over the steps in working that out into the polynomial form...
Multiplying out the factors containing the x variable (leavig the factor of 5 until the end, for simplicity's sake, although you can just do it all at once if you can keep track of things) you'll get:
Now back to our full equation, simplifying everything, and moving it all to the left side, leaving only 0 on the right:
At this point, we can simplify things ever-so-slightly by factoring out a -1:
I'll leave the rest up to you (don't want to do all of this poblem for you...lol), but by plugging in the correct answer of 4, it works out, so at least you know it's right so far...lol