1) x-2 x+3 _____ =____ x+2 x-42) 8y-5 9y _____ =

1) (x 2)/(x + 3) =  (x + 2)/(x 4);

Умножим накрест.

(x + 3) * (x + 2) = (x 2) * (x 4);

x^2 + 2 * x + 3 * x + 6 = x^2 4 * x 2 * x + 8;

x^2 + 5 * x + 6 = x^2 6 * x + 8;

5 * x + 6 * x = = 8 6;

11 * x = 2;

x = 2/11.

2) (8 * y 5)/(9 * y)  = y/(y + 2);

9 * y^2 = (8 * y 5) * (y + 2);

9 * y^2 = 8 * y^2 + 16 * y 5 * y 10;

y^2 11 * y + 10 = 0;

D = 121 4 * 1 * 10 = 81 = 9^2;

y1 = (11 + 9)/2 = 20/2 = 10;

y2 = (11 9)/2 = 2/2 = 1.

3) x^2 + 3 = 2  * x^2 + 1;

x^2 + 3 -  2 * x^2 1 = 0;

-x^2 + 2 = 0;

x^2 = -2;

Нет корней.

4) 3/(x^2 + 2 * x) = 1/15;

x^2 + 2 * x = 45;

x^2 + 2 * x 45 = 0;

D = 4 4 * 1 * (-45) = 184;

x1 = (-2 + 184^0.5)/2;

x2 = (-2 184^0.5)/2.

5) x + 2 = 4 * x + 1; 

x 4 * x = 1 2;

-3 * x = -1;

x = 1/3.

6) (x^2 5)/(x 1) = (7 * x + 10)/9; 

9 * x^2 45 = 7* x^2 + 10 * x 7 * x 10;

2 * x^2 3 * x + 35 = 0;

D = 9 4 * 2 * 35;

Нет корней.