1) x^2 4x/x^2+7x : 24-6x/49-x^2 2) y^3-16y/2y+18 : 4-y/y^2+9y 3) (a+b)^2-2ab/4a^2 : a^2+b^2/ab 4) 5c^3-5/c+2 : (c+1)^2-c/13c+26

Сократим дроби и упростим выражение:

1) (x^2  - 4 * x)/(x^2 + 7 * x) : (24 – 6 * x)/(49 - x^2)  =  (x * (х  - 4))/(х * (х + 7)) * (7 – x) * (7 + x)/(6 * (4 – х)) =  (1 * (-1))/(1 * 1) * (7 – x) * 1/(6 * 1) = -(7 – х)/6 = (х – 7)/6;  

2) (y^3 – 16 * y)/(2 * y + 18) : (4 – y)/(y^2 + 9 * y) = (y^3 – 16 * y)/(2 * y + 18) * (y^2 + 9 * y)/(4 – y)  = (y * (y – 4) * (y + 4))/(2 * (y + 9)) * (y * (y + 9))/(4 – y)  = - (y * (y + 4))/(2) * (y)  = -y^2 * (y + 4)/2;

3) ((a + b)^2 – 2 * a * b)/(4 * a^2) : (a^2 + b^2)/(a * b) = (a^2 + b^2)/(4 * a^2) * (a * b)/(a^2 + b^2)  = ¼;

4) (5 * c^3 – 5)/(c + 2) : ((c + 1)^2 – c)/(13 * c + 26) = 5 * (c – 1) * (c^2 + c + 1)/(c + 2) * 13 * (c + 2)/(c^2 + c + 1) = 5 * (c – 1) * 13  = 65 * (c – 1).