Question

5/ y-3 + 1/ y+3 - 4y-18/y^2 - 9 help пацани

Answer 1

Відповідь: 2у+30/у^2-9

Пояснення:

Answer 2

Sure, I'd be happy to help you simplify the expression! Let's take it step by step:

The given expression is:

(5 / (y - 3)) + (1 / (y + 3)) - (4(y - 18) / (y^2 - 9))

Step 1: Factor the denominators:

y^2 - 9 = (y - 3)(y + 3)

Step 2: Find the least common multiple (LCM) of the denominators:

LCM = (y - 3)(y + 3)

Step 3: Rewrite each fraction with the common denominator:

(5 * (y + 3) / LCM) + (1 * (y - 3) / LCM) - (4(y - 18) * (y + 3) / LCM)

Step 4: Combine the numerators over the common denominator:

(5y + 15 + y - 3 - 4(y^2 - 18y + 3y - 54)) / LCM

Step 5: Simplify the terms in the numerator:

(6y + 12 - 4y^2 + 72) / LCM

Step 6: Combine like terms:

(-4y^2 + 6y + 84) / LCM

Step 7: Factor out common terms from the numerator, if possible:

-2(2y^2 - 3y - 42) / LCM

Step 8: Factor the quadratic expression in the parentheses:

-2(2y + 7)(y - 6) / LCM

So, the simplified expression is:

-2(2y + 7)(y - 6) / ((y - 3)(y + 3))