38.5. Упростите дробно-рациональное выражение
1)х⁷+х⁵/х⁴+х²
2)у⁷+у⁹/у⁴+у²
3)а⁷-а¹⁰/а⁵-а²
4)х⁶-х⁴/х³+х²
5)а-2b/2b-a
6)4(a-b)²/2b-2a
7)(-a-b)²/a+b
8)(a-b)²/(b-a)
1)х⁷+х⁵/х⁴+х²
2)у⁷+у⁹/у⁴+у²
3)а⁷-а¹⁰/а⁵-а²
4)х⁶-х⁴/х³+х²
5)а-2b/2b-a
6)4(a-b)²/2b-2a
7)(-a-b)²/a+b
8)(a-b)²/(b-a)
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1) x⁷+x⁵/x⁴+x² = x⁵(x²+1)/x²(x²+1) = x⁵/x² = x³
2) y⁷+y⁹/y⁴+y² = y⁷(1+y²)/y²(y²+1) = y⁷/y² = y⁵
3) a⁷-a¹⁰/a⁵-a² = a⁷(1-a³)/a²(a³-1) = a⁷(1-a³)/(-a²(1-a³) = a⁷/(-a²) = -a⁵
4) x⁶-x⁴/x³+x² = x⁴(x²-1)/x²(x+1) = x⁴(x-1)(x+1)/x²(x+1) = x²(x-1) = x³ - x²
5) a-2b/2b-a = a-2b/(-(a-2b)) = -1
6) 4(a-b)²/2b-2a = 4(a-b)(a-b)/2(b-a) = 4(a-b)(a-b)/(-2(a-b)) = 4(a-b)/(-2) = -2(a-b) = 2b-2a
7) (-a-b)²/a+b = (-a-b)(-a-b)/-(-a-b) = (-a-b)/(-1) = a+b
8) (a-b)²/(b-a) = (a-b)(a-b)/(-(a-b)) = (a-b)/(-1) = b-a