1)x/(a+b) = a/(a^2-b^2)
x/(a+b) = a/(a-b)(a+b)
x*(a-b) = a
x=a/(a-b)
2)(a^2 - b^2)/x = (a^2 - 2ab +b^2)/b
x = (a^2 - b^2):(a^2 - 2ab +b^2)/b
x = (a^2 - b^2)*b/(a^2 - 2ab +b^2)
x = (a-b)(a+b)b/(a-b)^2 = (a+b)b/(a-b) = (ab+b^2)(a-b)
3) (a^4-a)/(2a^2-2a) = (a^2+a+1)/x
a(a^3-1)/2a(a-1) = (a^2+a+1)/x
x = (a^2+a+1) : a(a^3-1)/2a(a-1) =
= (a^2+a+1) * 2a(a-1)/ a(a^3-1) =
= 2(a^3+a^2+a-a^2-a-1)/(a^3-1) = 2(a^3-1)/(a^3-1) = 2
x=2
7х²-7 = 7(х²-1)= 7(х-1)(х+1)
а³-64а = а (а²-64)= а(а-8)(а+8)
5а³-5в³= 5(а³-в³) = 5 (а-в)(а²+ав+в²)
х²+2ху+у²-z² = (x-y)²-z² = (x-y-z)(x-y+z)