Question

Решите плиз(6x^2+18x^4)/(12x^3)(25y^(2)-4)/(25y+10) (9-a^(2))/a^(2)+6a+9

Answer 1

(6x^2+18x^4)/(12x^3)=(6x^2(1+3x^2))/ (12x^3)=( 1+3x^2) /2x

(25y^(2)-4)/(25y+10)=((5y-2)(5y+2))/(5(5y+2)) =(5y-2)/2

(9-a^(2))/a^(2)+6a+9=((3-a)(3+a)) / ((3+a)(3+a)) =(3-a)/(3+a)

Answer 2

To solve the expression (6x^2 + 18x^4)/(12x^3)(25y^2 - 4)/(25y + 10) + (9 - a^2)/a^2 + 6a + 9, let's break it down into smaller steps.

Step 1: Simplify the expression within parentheses Let's start by simplifying the expression within the first set of parentheses, (6x^2 + 18x^4)/(12x^3).

To simplify this expression, we can factor out the common terms from the numerator and denominator:

6x^2 + 18x^4 = 6x^2(1 + 3x^2)

12x^3 = 12x^3(1)

Now, we can cancel out the common terms:

(6x^2 + 18x^4)/(12x^3) = 6x^2(1 + 3x^2)/12x^3(1) = (1 + 3x^2)/(2x)

Step 2: Simplify the expression within the second set of parentheses Next, let's simplify the expression within the second set of parentheses, (25y^2 - 4)/(25y + 10).

Again, we can factor out the common terms from the numerator and denominator:

25y^2 - 4 = (5y)^2 - 2^2 = (5y - 2)(5y + 2)

25y + 10 = 5(5y + 2)

Now, we can cancel out the common terms:

(25y^2 - 4)/(25y + 10) = (5y - 2)(5y + 2)/(5(5y + 2)) = (5y - 2)/5

Step 3: Simplify the remaining terms Now, let's simplify the remaining terms in the expression:

(9 - a^2)/a^2 + 6a + 9

We can combine like terms:

(9 - a^2)/a^2 + 6a + 9 = 9/a^2 - a^2/a^2 + 6a + 9 = (9 - a^2 + 6a^3 + 9a^2)/a^2 = (15 + 8a^2)/a^2

Step 4: Combine the simplified terms Finally, let's combine the simplified terms from Step 1, Step 2, and Step 3:

(1 + 3x^2)/(2x) * (5y - 2)/5 + (15 + 8a^2)/a^2

To multiply fractions, we multiply the numerators together and the denominators together:

[(1 + 3x^2)(5y - 2)] / [2x * 5] + (15 + 8a^2)/a^2

Simplifying further, we get:

(5y + 15x^2 - 2 - 3x^2) / (10x) + (15 + 8a^2)/a^2

Combine like terms:

(12x^2 + 5y - 2) / (10x) + (15 + 8a^2)/a^2

This is the simplified version of the expression (6x^2 + 18x^4)/(12x^3)(25y^2 - 4)/(25y + 10) + (9 - a^2)/a^2 + 6a + 9.