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

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

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