Question

Сократите дробь (подробно расписывая):
1) (x^2-y^2):(x+y)^2
2) (x-y)^2:(x^2-y^2)
3) (x^2-9):(x^2+6x+9)
4) (x^2-10x+25):(x^2-25)

Answer 1

1)(x²-y²):(x+y)²=(x+y)(x-y):(x+y)(x+y)=(x-y):(x+y) , x+y≠0

2)(x-y)²:(x²-y²)=(x-y)(x-y):(x+y)(x-y)=(x-y):(x+y) , x+y≠0

3)(x²-9):(x²+6x+9)=(x²-3²):(x+3)²=(x+3)(x-3):(x+3)(x+3)=(x-3):(x+3), x≠-3

4)(x²-10x+25):(x²-25)=(x-5)²:(x+5)(x-5)=

=(x-5):(x+5) , x≠5,x≠-5

(A²-B²=(A+B)(A-B) , A²+2AB+B²=(A+B)²)