РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 159

159. Виконайте дії: 1) a^3/(a+b) + b^3/(a+b) = (a^3+ b^3)/(a+b) = ((a+b)(a^2- ab+ b^2))/(a+b) = a2 – ab + b2; 2) q^3/(p-q) – p^3/(p-q) = (q^3- p^3)/(p-q) = ((q-p)(q^2- qp+ p^2))/(p-q) = (-(p-q)(q^2+ qp+ p^2))/(p-q) = –q2 – qp – p2; 3) 〖2x〗^3/(x+y) – (x^3- y^3)/(x+y) = (〖2x〗^3- x^3+ y^3)/(x+y) = (x^3+ y^3)/(x+y) = ((x+y)(x^2- xy+ y^2))/(x+y) = x2 – xy + y2. 4) 27/(x-3) – x^3/(x-3) = 〖27-x〗^3/(x-3) = (〖(3-x)(9+3x+x〗^2))/(x-3) = (-(x-3)(9+3x+ x^2))/(x-3) = –9 – 3x – x2; 5) 8/(a-2) – a^3/(a-2) = 〖8-a〗^3/(a-2) = ((2-a)(4+2a+ a^2))/(a-2) = (-(a-2)(4+2a+ a^2))/(a-2) = –4 – 2a – a2. 6) a/(a^3+ b^3 ) + b/(a^3+ b^3 ) = (a+b)/(a^3+ b^3 ) = (a+b)/(〖(a+b)(a〗^2- ab + b^2)) = 1/(a^2- ab + b^2 ); 7) b/(b^3- c^3 ) – b/(b^3- c^3 ) = (c-b)/(b^3- c^3 ) = (-(b-c))/(〖(b-c)(b〗^2+ bc + c^2)) = –1/(b^2+ bc + c^2 ); 8) 1/(x^3+ 8) + (1+x)/(x^3+ 8) = (1+1+x)/(x^3+ 8) = (2+x)/(x^3+ 8) = 1/(x^2- 2x+4); 9) (a^2+ b^2)/(a^3+ b^3 ) – ab/(a^3+ b^3 ) = (a^2+ b^2- ab)/(〖(a+b)(a〗^2- ab + b^2)) = 1/(a+b); 10) c^2/(b^3- c^3 ) + 〖bc+b〗^2/(b^3- c^3 ) = (c^2+ bc+ b^2)/(b^3- c^3 ) = (c^2+ bc+ b^2)/(〖(b-c)(b〗^2+ bc + c^2)) = 1/(b-c).