ГДЗ Алгебра 8 клас Мерзляк (2025)

Спростіть вираз:

1) (a+ 7^(\3))/12 + (a-4^(\4))/9 = (3(a+7)+4(a-4))/36 = (3a+21+4a-16)/36 = (7a+5)/36;
2) (2b-7c^(\5))/6 – (3b+2c^(\2))/15 = (5(2b-7c)-2(3b+2c))/30 = (10b-35c-6b-4c)/30 = (4b-39c)/30;
3) (3x- 2^(\y))/x – (3y- 1^(\x))/y = (y(3x-2)- x(3y-1))/xy = (3xy-2y-3xy+ x)/xy = (x-2y)/xy;
4) (6p+ 1^(\3))/p – (2p+ 8^(\1) )/3p = (3(6p+1)-(2p+8))/3p = (18p+3-2p-8)/3p = (16p-5)/3p;
5) (5m-n^(\1) )/14m – (m-6n^(\2))/7m = ((5m- n)-2(m-6n))/14m = (5m- n-2m+12n)/14m = (3m+11n)/14m;
6) (x+ 4^(\y))/11x – (y-3^(\x) )/11y = (y(x+4)-x(y-3))/11xy = (xy+4y- xy+3x)/11xy = (4y+3x)/11xy;
7) (a+ b^(\c))/ab + (a-c^(\b) )/ac = (c(a+ b)+ b(a- c))/abc = (ac+ bc+ ab- bc)/abc = (ac+ ab)/abc;
8) (k+4^(\k) )/k – (3k- 4^(\1))/k^2 = (k(k+4)+(3k-4))/k^2 = (k^2+4k+3k-4)/k^2 = (k^2+7k-4 )/k^2 ;
9) (x-y^(\y) )/x^3 – (y-x^(2\x))/(x^2 y) = (y(x- y)-x(y- x^2))/(x^3 y) = (yx- y^2-xy+ x^3)/(x^3 y) = (x^3-y^2 )/(x^3 y);
10) (c+ d^(\c^2 ))/(cd^4 ) – (c^2-8d^(\d))/(c^3 d^3 ) = (c^2 (c+ d)- d(c^2-8d))/(c^3 d^4 ) = (c^3+c^2 d- dc^2+8d^2)/(c^3 d^4 ) = (c^3+8d^2)/(c^3 d^4 ).