(-5-1,5):(-5*1,5)=-6,5:(-7,5)=-65/10:(-75/10)=-65/10*(-10/75)=13/15
1)3(y-1)²+6y=3(y²-2y+1)+6y=3y²-6y+3+6y=3y²+3
2)8c+4(1-c)²=8c+4(1-2c+c²)=8c+4-8c+4c²=4+4c²
3)4ab+2(a-b)²=4ab+2(a²-2ab+b²)=4ab+2a²-4ab+2b²=2a²+2b²
4)3(x+y)²-6xy=3(x²+2xy+y²)-6xy=3x²+6xy+3y²-6xy=3x²+3y²
5)27.3ˇ4=3ˇ3.3ˇ4=3ˇ7=3.3.3.3.3.3.3=9.9.9.3=729.3=2187
6)(a³.b².c)ˇ4=aˇ12 . bˇ8 .cˇ4
1.
1) (6a/(2a+5)-16a/(4a²+20a+25)=6a/(2a+5)-16a/((2a)²+2*2a*5+5²)=
=6a/(2a+5)-16a/(2a+5)²=(6a*(2a+5)-16a)/(2a+5)²=(12a²+30a-16a)/(2a+5)²=
=(12a²+14a)/(2a+5)²=2a*(6a+7)/(2a+5)².
2) 2a*(6a+7)/(2a+5)²:(6a+7)/(4a²-25)=2a*(6a+7)*(2a+5)*(2a-5)/((6a+7)*(2a+5)²)=
=2a*(2a-5)/(2a+5).
3) 2a*(2a-5)/(2a+5)+(10a-25)/(2a+5)=(2a*(2a-5)+5*(2a-5))/(2a+5)=
=(2a-5)*(2a+5)/(2a+5)≡2a-5.
2.
1) 5x/(x-10)+20x/(x²-20x+100)=5x/(x-10)+20x/(x-10)²=(5x*(x-10)+20x)/(x-10)²=
=(5x²-50x+20x)/(x-10)²=(5x²-30x)/(x-10)²=5x*(x-6)/(x-10)².
2) 5x*(x-6)/(x-10)²:(4x-24)/(x²-100)=5x*(x-6)*(x-10)*(x+10)/((x-10)²*4*(x-6))=
=(5x*(x+10))/(4*(x-10)).
3) (5x*(x+10))/(4*(x-10))-25x/(x-10)=(5x²+50x-100x)/(4*(x-10))=
=(5x²-50x)/(4*(x-10))=5x*(x-10)/(4*(x-10))≡5x/4.