Question

Сократите дробь x^6+x^4 / x^4+x^2 2) x^6-x^8 / x^4-x^2 3) m^7-m^10 / m^9-m^3 4) a^6-a^4 / ^3+A^2

Answer 1

1) =х^4(x²+1)/x²(x²+1)=x²
  2)=x^6(1-x²)/x²(x²-1)= -x^4
  3) =m^7(1-m³)/m³(m^6-1)=m^4(1-m³)/-(1-m³)(1+m³)=-m^4/1+m³
  4)  =a^4(a²-1)/a²(a+1)=(a+1)(a-1)/(a+1)=a-1

Answer 2

1. To simplify the fraction (x^6 + x^4) / (x^4 + x^2), we can factor out common terms in the numerator and denominator: x^6 + x^4 = x^4(x^2 + 1) x^4 + x^2 = x^2(x^2 + 1) Now we can cancel out the common factor of (x^2 + 1): (x^4(x^2 + 1)) / (x^2(x^2 + 1)) = x^4 / x^2 = x^(4-2) = x^2

2. For the fraction (x^6 - x^8) / (x^4 - x^2), we can again factor out common terms: x^6 - x^8 = x^6(1 - x^2) x^4 - x^2 = x^2(x^2 - 1) Now we can cancel out the common factor of (x^2 - 1): (x^6(1 - x^2)) / (x^2(x^2 - 1)) = x^6 / x^2 = x^(6-2) = x^4

3. In the fraction (m^7 - m^10) / (m^9 - m^3), we can factor out common terms: m^7 - m^10 = m^7(1 - m^3) m^9 - m^3 = m^3(m^6 - 1) Now we can cancel out the common factor of (m^6 - 1): (m^7(1 - m^3)) / (m^3(m^6 - 1)) = m^7 / m^3 = m^(7-3) = m^4

4. The fraction (a^6 - a^4) / (^3 + A^2) seems to have some missing information or formatting issues. Please provide the correct expression or clarify the denominator.