1)a^2+ 2ab + b^2/a^2– b^2
2)x^2 - 2x+1\x^2 - 1
3)3a^-6ab+3b^2\6a^2 - 6b^2
4)5m^2 +10mn+5n^2 \15m^2 - 15n^2

Simplifying

4x3 + -81x = 0

Reorder the terms:

-81x + 4x3 = 0

Solving

-81x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.

x(-81 + 4x2) = 0

Factor a difference between two squares.

x((9 + 2x)(-9 + 2x)) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying

9 + 2x = 0

Solving

9 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.

9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0

0 + 2x = 0 + -9

2x = 0 + -9

Combine like terms: 0 + -9 = -9

2x = -9

Divide each side by '2'.

x = -4.5

Simplifying

x = -4.5

Subproblem 3

Set the factor '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying

-9 + 2x = 0

Solving

-9 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.

-9 + 9 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0

0 + 2x = 0 + 9

2x = 0 + 9

Combine like terms: 0 + 9 = 9

2x = 9

Divide each side by '2'.

x = 4.5

Simplifying

x = 4.5

Solution

x = {0, -4.5, 4.5}

1) При делении на 4 дают остаток 2

Последовательность можно записать в виде:

4n+2

Первые пять членов последовательности при n=1; 2; 3; 4; 5

6, 10, 14, 18, 22

2) При делении на 7 дают остаток 1

Последовательность можно записать в виде:

7n+1

Первые пять членов последовательности при n=1; 2; 3; 4; 5:

8, 15, 22, 29, 36

3) При делении на 5 дают остаток 3

Последовательность можно записать в виде:

5n+3

Первые пять членов последовательности при n=1; 2; 3; 4; 5:

8, 13, 18, 23, 28

4) При делении на 9 дают остаток 8

Последовательность можно записать в виде:

9n+8

Первые пять членов последовательности при n=1; 2; 3; 4; 5:

17, 26, 35, 44, 53