Розділ 1. РАЦІОНАЛЬНІ ВИРАЗИ » 7.10

Спростіть вираз: 1) 36/(a-3) : ((a+3)/(a-3) – (a-3)/(a+3) + 36/(a^2- 9)) = 3. 1. (a+3)/(a-3) – (a-3)/(a+3) + 36/(a^2- 9) = ((a+3)^2-(a-3)^2+36)/((a-3)(a+3)) = (a^2+ 6a+9- a^2+6a-9+36)/((a-3)(a+3)) = (12a+36)/((a-3)(a+3)); 2. 36/(a-3): (12a+36)/((a-3)(a+3)) = (36(a-3)(a+3))/((a-3) • 12(a+3)) = 3. 2) ((2x+ y)/(x-2y) + (2x- y)/(x+2y)) • (x^2- 4y^2)/(x^2+ y^2 ) = 4. 1. (2x+ y)/(x-2y) + (2x- y)/(x+2y) = ((2x+ y)(x+2y)+(2x- y)(x-2y))/((x-2y)(x+2y)) = (2x^2+4xy+ xy+2y^2+2x^2-4xy- xy+2y^2)/(x^2- 4y^2 ) = (4x^2+4y^2)/(x^2- 4y^2 ). 2. (4x^2+4y^2)/(x^2- 4y^2 ) • (x^2- 4y^2)/(x^2+ y^2 ) = (4(x^2 + y^2)(x^2 -4y^2))/((x^2 -4y^2)(x^2 + y^2)) = 4.