Вправи 101 - 200 » 167 (4-6)

4) (1/(a^2- 4ab+4b^2 ) – 1/(4b^2- a^2 )) : 2a/(a^2- 4b^2 ) = (1^(\a+2b)/((a-2b)^2 ) + 1^(\a-2b)/((a-2b)(a+2b))) • ((a-2b)(a+2b))/2a = (a+2b+a-2b)/((a-2b)^2 (a+2b)) • ((a-b)(a+2b))/2a = (2a(a-2b)(a+2b))/((a-2b)^2 (a+2b) • 2a) = 1/(a-2b); 5) ((a-8)/(a^2- 10a+25) – a/(a^2- 25)) : (a-20)/((a-5)^2 ) = ((a- 8^(\a+5))/((a-5)^2 ) – a^(\a-5)/((a-5)(a+5))) : (a-20)/((a-5)^2 ) = ((a+5)(a-8)- a(a-5))/((a-5)^2 (a+5)) • ((a-5)^2)/(a-20) = ((a^2- 8a+5a-40- a^2+ 5a)(a-5)^2)/((a- 5)^2 (a+5)(a-20)) = (2a-40)/((a+5)(a-20)) = (2(a-20))/((a+5)(a-20)) = 2/(a+5); 6) ((2x+1)/(x^2+ 6x+9) – (x-2)/(x^2+ 3x)) : (x^2+ 6)/(x^3- 9x) = ((2x+ 1^(\x))/((x+3)^2 ) – (x- 2^(\x+3))/(x(x+3)):(x^2+ 6)/(x^3- 9x) = (x(2x+1)- (x+3)(x-2))/(x(x+3)^2 ) • (x(x-3)(x+3))/(x^2+ 6) = (2x^2+ x-(x^2- 2x+3x-6))/(x(x+3)^2 ) • (x(x-3)(x+3))/(x^2+ 6) = ((2x^2+ x- x^2- x+6) • x(x-3)(x+3))/(x(x+3)^2 (x^2+ 6)) = ((x^2+ 6)(x-3))/((x+3)(x^2+ 6)) = (x-3)/(x+3).