Question

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

Answer 1

ответ: ЧИСЛИТЕЛЬ:   -х(в 2-ой степени)-3х+16

ЗНАМЕНАТЕЛЬ: х

Answer 2

To simplify the expression, let's find a common denominator for the three fractions:

The common denominator for the three fractions is (x^2 - 9), which can be factored as (x + 3)(x - 3).

Now, we'll rewrite each fraction with the common denominator:

1. 3/(x - 3): Since the common denominator is (x + 3)(x - 3), we'll multiply both the numerator and denominator by (x + 3) to get: (3 * (x + 3))/((x + 3)(x - 3))

2. (x + 15)/(x^2 - 9): We already have the common denominator, so no need to modify this fraction.

3. 2/x: To express this fraction with the common denominator, we'll multiply both the numerator and denominator by (x + 3): (2 * (x + 3))/((x + 3)(x - 3))

Now, the expression becomes:

[(3 * (x + 3))/((x + 3)(x - 3))] - [(x + 15)/(x^2 - 9)] - [(2 * (x + 3))/((x + 3)(x - 3))]

Next, let's combine the fractions:

To combine the fractions, we need to find a common denominator for the first and third fractions, which is (x + 3)(x - 3). Once we have that, we can combine the fractions into one.

[(3 * (x + 3) - (x + 15) - (2 * (x + 3)))/((x + 3)(x - 3))]

Now, let's simplify the expression:

[3x + 9 - x - 15 - 2x - 6)/((x + 3)(x - 3))]

Combine like terms in the numerator:

[3x - x - 2x + 9 - 15 - 6)/((x + 3)(x - 3))]

Simplify further:

(0x - 12)/((x + 3)(x - 3))

Simplify the numerator (0x - 12 = -12):

-12/((x + 3)(x - 3))

So, the simplified expression is:

-12/((x + 3)(x - 3))