Problem:

25-x^2 6
------ * ---
12 5-x
What I Got:
5-x
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2
*Please Check My Work And Tell Me If I am Correct or wrong.If I am wrong please help me as much as possible.Thank you~

Wrong. When are you going to factor the 25-x^2 ?

The 5-x then will divide out.

oh...so then will it be:
(5+x)
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2

You're on the right track! Let's go through the solution step by step:

1) Start by factoring the expression 25 - x^2. This is a difference of squares, so we can factor it as (5 + x)(5 - x).

2) Rewrite the given expression with the factored form of 25 - x^2 and simplify:
(5 - x)(5 + x) / (12)(5 - x)

Now, we can see that (5 - x) appears in both the numerator and denominator, so we can cancel it out:

(5 - x)(5 + x) / (12)(5 - x) = (5 + x) / 12

Therefore, the simplified expression is (5 + x) / 12.

You made a small mistake in your calculation by dividing (5 - x) by 2 instead of canceling it out. So the correct answer is:

(5 + x) / 12

Well done for trying, and keep up the good work! If you have any further questions, feel free to ask.