Verified answer

1. x^2-1=0,

(x-1)(x+1)=0,

x-1=0, x1=1,

x+1=0, x2=-1.

2. (a^2-1)/(1-a)=(a-1)(a+1)/(a-1)=a+1.

3. (x^2+1)/(x+1) + 2x/(x+1)=(x^2+1+2x)/(x+1)=(x+1)^2/(x+1)=x+1.

4. (x+y)^2/(8x) : (x^2-y^2)/(2y) = (x+y)^2/(8x) * 2y/(x^2-y^2) = (x+y)^2/(4x) * y/((x-y)(x+y)) = (x+y)/(4x) * y/(x-y) = y(x+y)/(4x(x-y)) = (xy+y^2)/(4x^2-4xy).

5. (x^(-2))^(-3)*x^(-8)=x^6 * x^(-8)=x^(-2),

(1/5)^(-2)=5^2=25,

6. (x-3)/2 - 1 = x,

x-3-2=2x,

-x=5,

x=-5.

7. х р. - 1 м подкладочной ткани, 5х р. - 1 м шерстяной ткани,

15х-4х=330.