Question

Сократить дробь А) 3x+15/4x+20 Б) x^2+10x+25/x^2-25

Answer 1

Вот ответ второго Б)

Answer 2

To simplify the given fractions, let's factorize the numerators and denominators where possible and then cancel out common factors:

A) $\frac{3x+15}{4x+20}$

Step 1: Factorize the numerator and denominator: Numerator: $3x + 15 = 3(x + 5)$ Denominator: $4x + 20 = 4(x + 5)$

Step 2: Cancel out the common factor in the numerator and denominator: $\frac{3x + 15}{4x + 20} = \frac{3(x + 5)}{4(x + 5)}$

Step 3: Further simplify if possible: Since there are no more common factors to cancel out, the fraction is already in its simplest form. Therefore, the simplified fraction is: $\frac{3x + 15}{4x + 20} = \frac{3(x + 5)}{4(x + 5)}$

B) $\frac{x^2 + 10x + 25}{x^2 - 25}$

Step 1: Factorize the numerator and denominator: Numerator: $x^2 + 10x + 25 = (x + 5)(x + 5) = (x + 5)^2$ Denominator: $x^2 - 25 = (x + 5)(x - 5)$

Step 2: Cancel out the common factor in the numerator and denominator: $\frac{x^2 + 10x + 25}{x^2 - 25} = \frac{(x + 5)^2}{(x + 5)(x - 5)}$

Step 3: Further simplify if possible: We can cancel out the common factor of $(x + 5)$ in the numerator and denominator: $\frac{(x + 5)^2}{(x + 5)(x - 5)} = \frac{x + 5}{x - 5}$

Therefore, the simplified fraction is: $\frac{x^2 + 10x + 25}{x^2 - 25} = \frac{x + 5}{x - 5}$