Zadanie 3
a)
\frac{8x^5y^2}{2xy^3}*\frac{12x^2y}{32x^3y^2}=\frac{3x^7y^3}{2x^4y^5}=\frac{3x^3}{2y^2}
x\ne 0 , y\ne0
b)
\frac{p^2q^7}{5pq^4}* \frac{15p^3q^2}{7pq}=pq^3*\frac{3p^2q}{7}=\frac{3p^3q^4}{7}
p\ne0 , q\ne 0
c)
\frac{1-3x}{2x+1}*\frac{4x^2-1}{1-9x^2}=\frac{(1-3x)(4x^2-1)}{(2x+1)(1-9x^2)}=\frac{4x^2-1-12x^3+3x}{2x-18x^3+1-9x^2}=\frac{-12x^3+4x^2+3x-1}{-18x^3-9x^2+2x+1}
2x+1\ne 0 => 2x\ne -1 => x\ne -\frac{1}{2}
i
1-9x^2\ne0 => -9x^2\ne -1 => 9x^2\ne1 => x^2\ne \frac{1}{9} => x\ne\sqrt{\frac{1}{9}} i x\ne -\sqrt{\frac{1}{9}}