Question

упростите выражение.
А)=b, B=-b, C=b 2/3-1, D=b^1/3-1​

Answer 1

$\Big (\frac{b^{\frac{1}{3}}}{b-1}+\frac{b}{b^{\frac{4}{3}}-b^{\frac{2}{3}}}\Big )\cdot \Big (b^{\frac{1}{3}}-1\Big )\cdot \frac{b-1}{b^{\frac{1}{3}}}=\\\\=\frac{b^{\frac{1}{3}}}{b-1}\cdot \Big (b^{\frac{1}{3}}-1\Big )\cdot \frac{b-1}{b^{\frac{1}{3}}}+\frac{b}{b^{\frac{2}{3}}\, (b^{\frac{2}{3}}-1)}\cdot \Big (b^{\frac{1}{3}}-1\Big )\cdot \frac{b-1}{b^{\frac{1}{3}}}=\\\\=b^{\frac{1}{3}}-1+\frac{b\cdot (b^{\frac{1}{3}}-1)\cdot (b-1)}{b\cdot (b^{\frac{1}{3}}-1)(b^{\frac{1}{3}}+1)}=b^{\frac{1}{3}}-1+\frac{b-1}{b^{\frac{1}{3}}+1}=$

$=\frac{(b^{\frac{1}{3}}-1)(b^{\frac{1}{3}}+1)+b-1}{b^{\frac{1}{3}}+1}=\frac{b^{\frac{2}{3}}-1+b-1}{b^{\frac{1}{3}}+1}=\frac{b^{\frac{2}{3}}+b-2}{b^{\frac{1}{3}}+1}$