Question

сократите дробь 1)а^4-b^4/a^2 +b^2 2)x^4-y^4/x^2-y^2 3)a^3-b^3/a^4-b^4 4)a^2+ab+b^2/a^3-b^3 Срочно 20 балов полный ответ

Answer 1

$1) frac{а^4-b^4}{a^2 +b^2 } = frac{(a^2 +b^2 )(a^2 - b^2) }{a^2 +b^2 } = \ = a^2 - b^2$

$2) frac{x^4-y^4}{x^2-y^2 } = frac{(x^2-y^2)(x^2 + y^2 )}{x^2-y^2 } = \ = {x}^{2} + {y}^{2}$

$3) frac{a^3-b^3}{a^4-b^4} = frac{(a - b)( {a}^{2} + ab + {b}^{2} )}{( {a}^{2} - {b}^{2} )({a}^{2} + {b}^{2})} = \ = frac{(a - b)( {a}^{2} + ab + {b}^{2} )}{( a + b)(a - b)({a}^{2} + {b}^{2})} = \ = frac{( {a}^{2} + ab + {b}^{2} )}{( a + b)({a}^{2} + {b}^{2})}$

$4) frac{a^2+ab+b^2}{a^3-b^3} = frac{a^2+ab+b^2}{(a - b)(a^2+ab+b^2)} = \ = frac{1}{a - b}$