Question

Сократи дробь x^2−25/x^2+2x−35 .

Answer 1

(х-5)(х+5)/(х+7)(х-5)=х+5/х+7

Answer 2

To simplify the fraction (x^2 - 25)/(x^2 + 2x - 35), we need to factor the numerator and denominator, if possible, and then cancel out common factors.

Step 1: Factor the numerator and denominator. Numerator (x^2 - 25): This is a difference of squares, so we can factor it as (x + 5)(x - 5).

Denominator (x^2 + 2x - 35): This quadratic expression can be factored. We look for two numbers that multiply to give -35 and add up to +2 (the coefficient of x). Those numbers are +7 and -5, so we can factor the denominator as (x + 7)(x - 5).

Step 2: Cancel out common factors. Now that we have factored both the numerator and the denominator, we can cancel out common factors. In this case, (x - 5) appears in both the numerator and the denominator, so it can be canceled out.

(x^2 - 25)/(x^2 + 2x - 35) = (x + 5)(x - 5) / (x + 7)(x - 5)

Step 3: Simplify the expression. After canceling out the common factor (x - 5), we are left with:

(x + 5) / (x + 7)

So, the simplified form of the fraction is (x + 5)/(x + 7).