Question

Сократить дробь 2y^2+8y-90/3y^2+6y-105

Answer 1

Ответ смотри на фото.

Answer 2

To simplify the fraction (2y^2 + 8y - 90) / (3y^2 + 6y - 105), we need to factor the numerator and denominator and then cancel out any common factors.

Step 1: Factor the numerator and denominator: Numerator: 2y^2 + 8y - 90 Denominator: 3y^2 + 6y - 105

Numerator factors: 2y^2 + 8y - 90 = 2(y^2 + 4y - 45)

To factor the quadratic expression in parentheses, we need to find two numbers whose product is -45 and whose sum is +4. The numbers are +9 and -5: y^2 + 4y - 45 = (y + 9)(y - 5)

Denominator factors: 3y^2 + 6y - 105 = 3(y^2 + 2y - 35)

To factor the quadratic expression in parentheses, we need to find two numbers whose product is -35 and whose sum is +2. The numbers are +7 and -5: y^2 + 2y - 35 = (y + 7)(y - 5)

Step 2: Cancel out the common factors: Now we can simplify the fraction by canceling out the common factors in the numerator and denominator: (2y^2 + 8y - 90) / (3y^2 + 6y - 105) = [2(y + 9)(y - 5)] / [3(y + 7)(y - 5)]

Since (y - 5) appears in both the numerator and denominator, we can cancel it out: = 2(y + 9) / 3(y + 7)

So, the simplified fraction is 2(y + 9) / 3(y + 7).