Question

Сократи дробь (x−3)^2/x^2+2x−15

Answer 1

$\frac{(x-3)^2}{ x^{2} +2x-15} = \frac{(x-3)^2}{(x-3)(x+5)} = \frac{x-3}{x+5}$

Answer 2

To simplify the given fraction, we'll start by factoring the numerator and denominator, and then cancel out common factors:

Given fraction: (x - 3)^2 / (x^2 + 2x - 15)

Step 1: Factor the numerator (x - 3)^2: (x - 3)^2 = (x - 3)(x - 3)

Step 2: Factor the denominator (x^2 + 2x - 15): We need to find two numbers whose product is -15 and sum is 2. The numbers are 5 and -3 because 5 * -3 = -15 and 5 + (-3) = 2.

So, we can rewrite the denominator as: x^2 + 2x - 15 = x^2 + 5x - 3x - 15 = (x^2 + 5x) + (-3x - 15) = x(x + 5) - 3(x + 5)

Step 3: Substitute the factored forms back into the fraction: (x - 3)^2 / (x^2 + 2x - 15) = (x - 3)(x - 3) / [x(x + 5) - 3(x + 5)]

Step 4: Cancel out the common factor (x + 5) in the denominator: (x - 3)^2 / (x^2 + 2x - 15) = (x - 3)(x - 3) / [(x + 5)(x - 3)]

Step 5: Cancel out the common factor (x - 3) in the numerator and denominator: (x - 3)^2 / (x^2 + 2x - 15) = (x - 3) / (x + 5)

So, the simplified form of the given fraction is (x - 3) / (x + 5).