simplify 3/x + 2/x-2 -2/x^2?
First, we find a common denominator among the fractions. This will involve finding the highest power of x by itself, and then each separate instance of x with a constant. For this problem: x^2(x-2) is the common denominator. Now, you can combine everything by multiplying each piece of the numerator by our common denominator (without the pieces that it already has).
The first term 3/X will be multiplied by x(x-2) because it already has the x term. The second term will be multiplied by x^2 because it already has the (x-2) term. The final piece will be multiplied by (x-2). Therefore, once we have done this, your problem will look something like:3(x(x-2))/(x^2(x-2))+2x^2/(x^2(x-2))-(2(x-2))/(x^2(x-2)).
Now that all of these denominators are the same we can combine them, and then we can carry out all the algebra in the numerator: (5x^2-8x+4)/(x^2(x-2)).
You can try to simplify this further by taking out common factors in the numerator and cancelling them out from the denominator. In this case, it doesn’t work out, but it’s always good to check and make sure that the problem is completely simplified.