Question

3/(x-3)-(x+15)/(x^2-9)-2/x

Answer 1

3/х-3 - х+15/(х-3)(х+3) - 2/х

3х(х+3)-х(х+15)-2(х-3)(х+3) / х(х-3)(х+3)

3х²+9х-х²-15х-2(х²-9) / х(х-3)(х+3)

3х²+9х-х²-15х-2х²+18 / х(х-3)(х+3)

0-6х+18 / х(х-3)(х+3)

-6(х-3) /  х(х-3)(х+3)

-6 / х(х+3)

Ответ

-6 / х² + 3х

Answer 2

To simplify the expression 3/(x-3) - (x+15)/(x^2-9) - 2/x, we need to find a common denominator for all the terms and then combine them.

Step 1: Find the common denominator. The common denominator for the three terms is (x-3)(x+3)(x).

Step 2: Rewrite each term with the common denominator. The first term, 3/(x-3), already has the common denominator, so we can leave it as it is. The second term, (x+15)/(x^2-9), can be rewritten as follows: (x+15)/(x^2-9) = (x+15)/[(x-3)(x+3)]

The third term, 2/x, can be rewritten as follows: 2/x = 2(x-3)(x+3)/[(x-3)(x+3)x]

Step 3: Combine the terms. Now, the expression becomes: 3/(x-3) - (x+15)/[(x-3)(x+3)] - 2(x-3)(x+3)/[(x-3)(x+3)x]

Step 4: Combine the numerators over the common denominator. To combine the numerators, we'll need to find a common denominator for the first two terms, which is (x-3)(x+3).

Now, the expression becomes: [3(x+3) - (x+15) - 2(x-3)(x+3)] / [(x-3)(x+3)x]

Step 5: Simplify the numerator. Expand the expression in the numerator: [3x + 9 - x - 15 - 2(x^2 - 9)] / [(x-3)(x+3)x] Simplify the terms: [2x - 2x^2 + 18] / [(x-3)(x+3)x]

Step 6: Factor out common terms if possible. Factor out 2 from the numerator: 2(x - x^2 + 9) / [(x-3)(x+3)x]

So, the simplified expression is: (2x - 2x^2 + 18) / [(x-3)(x+3)x]