Question

ПОМОГИТЕ,ПОЖАЛУЙСТА УПРОСТИТЬ! (егэ профиль)

Answer 1

$b^{0.5}=\sqrt{b}$
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1) $\frac{2+2b^{0.5}}{b^{1.5}-b^{0.5}}=$
$\frac{2*1+2*b^{0.5}}{b^{0.5}*b^1-1*b^{0.5}}=$
$\frac{2(1+b^{0.5})}{b^{0.5}*(b^{0.5*2}-1^2)}=$
$\frac{2(1+b^{0.5})}{b^{0.5}*(b^{0.5}-1)(b^{0.5}+1)}$
$=\frac{2}{b^{0.5}(b^{0.5}-1)}=\frac{2}{\sqrt{b}(\sqrt{b}-1)}$

2) $\frac{b^{-0.5}}{\sqrt{b}-1}:\frac{\sqrt{b}}{b-2\sqrt{b}+1}=$
$\frac{1}{\sqrt{b}(\sqrt{b}-1)}*\frac{(\sqrt{b}-1)^2}{\sqrt{b}}$
$=\frac{\sqrt{b}-1}{b}$

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

4) $\frac{b+1}{b\sqrt{b}-1}*(\sqrt{b}-1)=\frac{b+1}{b}$