when I tried to find solution of 1/(x-3) + 1/(x-9) = 1/(x-2) + 1/ (x-8) all terms of x are cancelled out why?

Is there any rule to find solution of this?plz guide me.

Your school subject is Math.

Don't know how you did to get them to cancel. Perhaps you can post your work so we can look at it.

Mean while, if you look at the function f(x), it has four vertical asymptotes at x=2,3,8,9 respectively.
It has one horizontal asymptote, y=0, evidenced by taking the limit of x in each term to ±&inf;.

You may or may not have root under these circumstances. In the particular case, there are two complex roots, which don't count in the ℝ domain.

Here's a link to the graph of the function:
http://img411.imageshack.us/img411/9915/1291291222.png

To understand why all the terms of x are cancelling out in the given equation: 1/(x-3) + 1/(x-9) = 1/(x-2) + 1/(x-8), we need to simplify the equation and find the common denominator.

To find the common denominator, we multiply each term by the respective denominators. In this case, the common denominator is (x-3)(x-9)(x-2)(x-8).

Let's simplify the equation step by step:

1/(x-3) + 1/(x-9) = 1/(x-2) + 1/(x-8)

Multiply each term by the respective denominators:

(x-3)(x-9)(x-2)(x-8) * [1/(x-3) + 1/(x-9)] = (x-3)(x-9)(x-2)(x-8) * [1/(x-2) + 1/(x-8)]

Now, when you simplify the left-hand side and the right-hand side, you'll notice that all the terms with x will cancel out.

The reason behind this cancellation is that the common denominator, (x-3)(x-9)(x-2)(x-8), contains all the factors (x-3), (x-9), (x-2), and (x-8). So, when you multiply each term by the respective denominators, the corresponding terms in both sides of the equation will contain the same factors and will cancel each other out.

Unfortunately, this cancellation does not give us any meaningful solution to the equation. It means that the original equation is an inconsistent equation, which implies that there are no values of x that satisfy the equation.

To find a solution to this equation, you need to look for any restrictions or assumptions stated in the problem. If there are none, then it can be concluded that there is no solution.

I hope this explanation helps! If you have any further questions, please let me know.