Question

Pomogite pojaluista srochno nado! algebra za 7 klass.sokratite drobi:1)3a^2 – 6ab + 3b^2/6a^2-6b^22)2a^3-2b^3/5a^2-5b^23)a^3-b^3/a^4-b^44)2a+4/a^3+85)3n^2-3m^2/6m^3+6n^36)x^6-x^8/x^4-x^2Zaranee vsem ogromnoe spasibo)

Answer 1

1) 74ab^3-36a^2b^2+3b^2-12a^3b+6a^4/2a^2-12b^2

2)8b^3-2a^3/25b^2-5a^2

3)b^2+ab+a^2/b^3+ab^2 +a^2b+a^3

4) 2a+4/a^3+8

5) n^2-3m^2/2n^3+74m^3

6)-x^4 

 

Answer 2

Simplifying Fractions

To simplify the given fractions, we can factorize the numerator and denominator and cancel out common factors. Let's simplify each fraction one by one.

1) 3a^2 - 6ab + 3b^2 / 6a^2 - 6b^2

To simplify this fraction, we can factorize the numerator and denominator:

Numerator: 3a^2 - 6ab + 3b^2 = 3(a^2 - 2ab + b^2) = 3(a - b)^2 Denominator: 6a^2 - 6b^2 = 6(a^2 - b^2) = 6(a - b)(a + b)

Now we can cancel out the common factor (a - b) from the numerator and denominator:

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

2) 2a^3 - 2b^3 / 5a^2 - 5b^2

To simplify this fraction, we can factorize the numerator and denominator:

Numerator: 2a^3 - 2b^3 = 2(a^3 - b^3) = 2(a - b)(a^2 + ab + b^2) Denominator: 5a^2 - 5b^2 = 5(a^2 - b^2) = 5(a - b)(a + b)

Now we can cancel out the common factor (a - b) from the numerator and denominator:

2(a - b)(a^2 + ab + b^2) / 5(a - b)(a + b) = 2(a^2 + ab + b^2) / 5(a + b)

3) a^3 - b^3 / a^4 - b^4

To simplify this fraction, we can factorize the numerator and denominator:

Numerator: a^3 - b^3 = (a - b)(a^2 + ab + b^2) Denominator: a^4 - b^4 = (a^2 - b^2)(a^2 + b^2) = (a - b)(a + b)(a^2 + b^2)

Now we can cancel out the common factor (a - b) from the numerator and denominator:

(a - b)(a^2 + ab + b^2) / (a - b)(a + b)(a^2 + b^2) = 1 / (a + b)

4) 2a + 4 / a^3 + 8

To simplify this fraction, we can't factorize the numerator and denominator further. So, the fraction remains as it is:

2a + 4 / a^3 + 8

5) 3n^2 - 3m^2 / 6m^3 + 6n^3

To simplify this fraction, we can't factorize the numerator and denominator further. So, the fraction remains as it is:

3n^2 - 3m^2 / 6m^3 + 6n^3

6) x^6 - x^8 / x^4 - x^2

To simplify this fraction, we can factorize the numerator and denominator:

Numerator: x^6 - x^8 = x^6(1 - x^2) = x^6(1 - x)(1 + x) Denominator: x^4 - x^2 = x^2(x^2 - 1) = x^2(x - 1)(x + 1)

Now we can cancel out the common factor (1 - x) from the numerator and denominator:

x^6(1 + x) / x^2(x - 1)(x + 1) = x^4(1 + x) / (x - 1)(x + 1)

I hope this helps! Let me know if you have any further questions.