Question

(а/(a-b)-(a+b)/a)*(a+b)/a

(b/(a-b)-b/(a+b))*(a-b)/b

(a/c+c/a-2)*1/(a-c)

 

 

 

 

 

 

 

Answer 1

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

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

3. $(frac{a}{c}+frac{c}{a}-2)*frac{1}{a-c}=frac{a^2+c^2-2ac}{ac}*frac{1}{a-c}=frac{(a-c)^2}{ac(a-c)}=frac{a-c}{ac}$