Question

1) 5+a/2a^2+1-2a/a; 2)4x+8/12x^3•3x/x+2; 3) (m+n)^2:m^2-n^2/8m; 4) 2-b/b+b-3/3b^2; 5)3c+9/6c•2c^4/c+3; 6)x^2-y^2/6y:(x-y)^2

Answer 1

Не уверена, возможно где-то ошиблась

Answer 2

1) 5+a/2a^2+1-2a/a:

To simplify the given expression, we can follow these steps:

First, let's simplify each term in the expression:

5 + a/2a^2 + 1 - 2a/a

Combine the constants:

5 + 1 = 6

Now, let's simplify the fraction a/2a^2:

a/2a^2 = 1/(2a)

Next, let's simplify the term -2a/a:

-2a/a = -2

Now, let's combine all the simplified terms:

6 + 1/(2a) - 2

The expression can be simplified to:

6 + 1/(2a) - 2

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2) 4x+8/12x^3•3x/x+2:

To simplify the given expression, we can follow these steps:

First, let's simplify each term in the expression:

4x + 8 / 12x^3 • 3x / (x + 2)

Combine the constant and the fraction:

4x + 8 / 12x^3

Now, let's simplify the term 3x / (x + 2):

3x / (x + 2)

Now, let's combine all the simplified terms:

(4x + 8) / (12x^3) • (3x / (x + 2))

The expression can be simplified to:

(4x + 8) / (12x^3) • (3x / (x + 2))

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3) (m+n)^2:m^2-n^2/8m:

To simplify the given expression, we can follow these steps:

First, let's simplify the numerator (m+n)^2:

(m+n)^2 = m^2 + 2mn + n^2

Now, let's simplify the denominator m^2-n^2:

m^2 - n^2 = (m+n)(m-n)

Now, let's simplify the fraction (m^2 + 2mn + n^2) / ((m+n)(m-n)):

(m^2 + 2mn + n^2) / ((m+n)(m-n))

Next, we have to divide by 8m:

(m^2 + 2mn + n^2) / ((m+n)(m-n)) / 8m

The expression can be simplified to:

(m^2 + 2mn + n^2) / ((m+n)(m-n) * 8m)

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4) 2-b/b+b-3/3b^2:

To simplify the given expression, we can follow these steps:

First, let's simplify each term in the expression:

2-b / b+b-3 / 3b^2

Now, let's simplify the terms:

(2-b) / (b-3) / (b+b) / 3b^2

Simplify the terms inside the fractions:

(2-b) / (b-3) / 2b / 3b^2

The expression can be simplified to:

(2-b) / (b-3) / 2b / 3b^2

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5) 3c+9/6c•2c^4/c+3:

To simplify the given expression, we can follow these steps:

First, let's simplify each term in the expression:

3c + 9 / 6c • 2c^4 / (c + 3)

Now, let's combine the constant and the fraction:

3c + 9 / 6c

Now, let's simplify the term 2c^4 / (c + 3):

2c^4 / (c + 3)

The expression can be simplified to:

(3c + 9) / 6c • 2c^4 / (c + 3)

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6) x^2-y^2/6y:(x-y)^2:

To simplify the given expression, we can follow these steps:

First, let's simplify the numerator x^2 - y^2:

x^2 - y^2 = (x+y)(x-y)

Now, let's simplify the denominator (x-y)^2:

(x-y)^2 = (x-y)(x-y)

Now, let's simplify the fraction (x+y)(x-y) / (6y) : (x-y)(x-y):

((x+y)(x-y) / (6y)) : ((x-y)(x-y))

The expression can be simplified to:

((x+y)(x-y) / (6y)) : ((x-y)(x-y))