Question

Сократи дробь x^2−25/x^2+3x−40.

Answer 1

Ответ:

Пошаговое объяснение:

Разложим на множители знаменатель. Для этого решим уравнение:

х²+3х-40=0

Д=3²+4*40=9+160=169=13²

х1=(-3+13)/2=5

х2=(-3-13)/2=-8

х²+3х-40=(х-5)(х+8)

(х²-25)/(х²+3х-40)=

=(х-5)(х+5)/(х-5)(х+8)= (х+5) / (х+8)

Answer 2

To simplify the fraction (x^2 - 25) / (x^2 + 3x - 40), we first factor the numerator and denominator, if possible, and then cancel out any common factors.

Step 1: Factor the numerator and denominator.

Numerator: x^2 - 25 can be factored as the difference of squares: (x + 5)(x - 5). Denominator: x^2 + 3x - 40 can be factored as (x + 8)(x - 5).

Step 2: Cancel out common factors.

Now, we can cancel out the common factor (x - 5) from both the numerator and the denominator:

(x + 5)(x - 5) / (x + 8)(x - 5).

Step 3: Simplify the expression.

After canceling the common factor (x - 5), the simplified expression is:

(x + 5) / (x + 8).