Question

Сократите дробь 15x^7y^5/6ab ; 18ab-6b/6ab ; a^2-1/3a+3

Answer 1

Первое задание:

\frac{15x^7y^5}{6ab}\\ \\\frac{5x^7y^5}{2ab}  Сократили 15 и 6 на 3.

Второе задание:

\frac{18ab-6b}{6ab}\\ \\\frac{6b*(3a-1)}{6ab}\\ \\\frac{b*(3a-1)}{ab}\\ \\\frac{3a-1}{a}

Третье задание:

\frac{a^2-1}{3a+3}\\ \\\frac{(a-1)*(a+1)}{3(a+1)}\\ \\\frac{a-1}{3}

Answer 2

To simplify each fraction, let's perform the required operations step-by-step:

1. Simplify the fraction (15x^7y^5) / (6ab):

First, look for common factors between the numerator and the denominator: Numerator: 15x^7y^5 Denominator: 6ab

Common factors: 3 (from 15 and 6), x^7 (from x^7 in the numerator), y^5 (from y^5 in the numerator), and b (from the "b" in the denominator).

Now, divide both the numerator and the denominator by these common factors: (15x^7y^5) / (6ab) = (3 * 5 * x^7 * y^5) / (3 * 2 * a * b) = (5x^7y^5) / (2ab)

2. Simplify the fraction (18ab - 6b) / (6ab):

Here, we can factor out the common term "6b" from the numerator: (18ab - 6b) = 6b * (3a - 1)

Now, the fraction becomes: (18ab - 6b) / (6ab) = (6b * (3a - 1)) / (6ab)

Next, we can cancel out the common factor "6b" in the numerator and denominator: (6b * (3a - 1)) / (6ab) = (3a - 1) / a

3. Simplify the fraction (a^2 - 1) / (3a + 3):

This fraction is already in its simplest form. There are no common factors to cancel out.

The simplified fractions are as follows:

1. (15x^7y^5) / (6ab) simplifies to (5x^7y^5) / (2ab)
2. (18ab - 6b) / (6ab) simplifies to (3a - 1) / a
3. (a^2 - 1) / (3a + 3) remains as (a^2 - 1) / (3a + 3)