РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 161 (5-8)

5) 125/〖(x-5)〗^2 – x^3/〖(x-5)〗^2 = 〖125-x〗^3/〖(x-5)〗^2 = (5^3- x^3)/〖(x-5)〗^2 = (〖(5-x)(25+5x+x〗^2))/〖(x-5)〗^2 = 〖25+5x+x〗^2/(5-x) = (x^2+ 5x+25)/(5-x); 6) 3/〖(x+2)〗^3 + (x^2+ 4x+1)/〖(x+2)〗^3 = (〖3+x〗^2+ 4x+1)/〖(x+2)〗^3 = (x^2+ 4x+4)/〖(x+2)〗^3 = 〖(x+2)〗^2/〖(x+2)〗^3 = 1/(x+2); 7) (32-14x)/〖(x-3)〗^2 – (26-12x)/〖(3-x)〗^2 = (32-14x)/〖(x-3)〗^2 – (26-12x)/〖(x-3)〗^2 = (32-14x-26+12x)/〖(x-3)〗^2 = (-2x+6)/〖(x-3)〗^2 = (-2(x-3))/〖(x-3)〗^2 = –2/(x-3); 8) (x^2+ 8y)/((x-4)(y+3)) + (4(x+2y))/((4-x)(3+y)) = (x^2+ 8y)/((x-4)(y+3)) – (4(x+2y))/((x-4)(y+3)) = (x^2+ 8y-4x-8y)/((x-4)(y+3)) = (x^2-4x)/((x-4)(y+3)) = (x(x-4))/((x-4)(y+3)) = x/(y+3).