1Wykonaj dzialania a x+3/x*x²/x-9 b x³-8/2x-7 : x²+2x+4/4x²-49 c 2x/x-4 : x²/x²-16 d 21x+x²/x⁴-1:x³-7x²/12x²-12

a) x+3/x*x²/x-9 = po skróceniu rzez x = (x+3)*x/(x-9) b) x³-8/2x-7 : x²+2x+4/4x²-49 = = ((x-2)(x² +4x +4))/(2x - 7) : (x² +2x +4)/(2x +7)(2x - 7) = ((x-2)(x² +4x +4))/(2x - 7) *(2x +7)(2x - 7)/ (x² +2x +4) = = po skróceniu przez (2x - 7) mamy: = (x-2)(x² +4x +4)*(2x +7)/(x² +2x +4) c)2x/x-4 : x²/x²-16 = 2x/(x-4) * (x-4)(x+4)/x² = = po skróceniu przez x oraz przez (x - 4) = 2*(x +4)/x d)21x+x²/x⁴-1:x³-7x²/12x²-12 = = x(21 +x)/(x-1)(x³ + x² +x +1) *12(x²-1)/7x² = =x(21 +x)/(x-1)(x³ + x² +x +1) * 12(x + 1)(x -1)/7x²= = po skróceniu przez x oraz (x-1) otrzymujemy: = (21 +x)/(x³ + x² + x + 1) * 12(x + 1 )/ 7x

a) (x+3)/x * x²/(x-9) = x(x+3)/(x-9) b) [(x³-8)/(2x-7)] : [(x²+2x+4)/(4x²-49)] = = [(x-2)(x²+2x +4) / (2x-7)] * [(2x-7)(2x+7)/(x²+2x+4)] = = (x-2)*(2x +7) c) [2x/(x-4)] : [x²/(x²-16)] = [2x/(x-4)] * [(x-4)(x+4)/x²] = = 2*(x+4) / x d) [(21x+x²)/(x⁴-1)] : [(x³-7x²)/(12x²-12)] = = [x(21+x)/(x²-1)(x²+1)] * [12(x²-1)/x²(x-7)] = = [(21 +x)/(x²+1)] * [12/x(x-7)]