Question

[tex]frac{c+3}{c^2}-frac{1}{c}\ frac{2}{x}+frac{3x-2}{x+1}\ frac{(a+x)^3}{4a}cdotfrac{10a(a-x)}{a^2-x^2}\ frac{3a^2}{b}:frac{b}{a^3}\ frac{2a-b}{a}cdotfrac{(a}{2a-b}+frac{a}{b})} [/tex

Answer 1

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

 

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

 

$frac{(a+x)^{3}}{4a}cdotfrac{10a(a-x)}{a^{2}-x^{2}}=frac{(a+x)(a+x)^{2}}{4a}cdotfrac{10a(a-x)}{(a-x)(a+x)}}=frac{10a(a-x)(a+x)(a+x)^{2}}{4a(a-x)(a+x)}}=frac{5(a+x)^{2}}{2}=2,5(a+x)^{2}$

 

$frac{3a^{2}}{b}:frac{b}{a^{2}}=frac{3a^{2}}{b}cdotfrac{a^{2}}{b}=frac{3a^{4}}{b^{2}}$

 

$frac{2a-b}{a}cdot(frac{a}{2a-b}+frac{a}{b})=frac{2a}{b}=2ab^{-1}$

 

1) $frac{a}{2a-b}+frac{a}{b}=frac{ab+a(2a-b)}{b(2a-b)}=frac{ab+2a^{2}-ab}{b(2a-b)}= frac{2a^{2}+(ab-ab)}{b(2a-b)}=frac{2a^{2}}{b(2a-b)}$

 

2) $frac{2a-b}{a}cdotfrac{2a^{2}}{b(2a-b)}=frac{2a}{b}=2ab^{-1}$