Question

Срочно! Допоможіть з алгеброю!

Answer 1

A)
1. 1-a/(1+a)=(1+a-a)/(1+a)=1/(1+a)
2. a/(ab+b)=a/(b*(a+1))
3. (1/(1+a)):(a/(b*(a+1))=1*b*(a+1)/((a+1)*a)=b/a.
б)
1. (9b²-4)/(4b²-4b+1)=(3b-2)(3b+2)/(2b-1)²
2. ((3b-2)(3b+2)/(2b-1)²):(3b-2)/(2b-1)=(3b-2)(3b+2)(2b-1)/((2b-1)²(3b-2))=
=(3b+2)/(2b-1)
3. ((3b+2)/(2b-1))+((b+3)/(1-2b))=((3b+2)/(2b-1))-((b+3)/(2b-1))=
=(3b+2-b-3)/(2b-1)=(2b-1)/(2b-1)=1.
в)
1. 16/(b²-16)=16/((b-4)(b+4)
2. (b²+4b)/(b²+8b+16)=b*(b+4)/(b+4)²=b/(b+4)
3. 16/((b-4)(b+4))+b/(b+4)=(16+b*(b-4)/((b-4)(b+4))=(b²-4b+16)/((b-4)(b+4))
4. (4-b)/(64-b³)=(b-4)/(b³-64)=(b-4)/((b-4)(b²-4b+16))=1/(b²-4b+16)
5. ((b²-4b+16/(b²-16))*(1/(b²-4b+16))=1/(b²-16).
г)
1. 1+1/(a-1)=(a-1+1)/(a-1)=a/(a-1)
2. 1-1/(a/(a-1)=1-(a-1)/a=(a-a+1)/a=1/a
3. 1/(1/a)=a.