Giải thích các bước giải:
a.Ta có:
$A=\dfrac{5x+3y}{6x-7y}$
$\to A=\dfrac{(5x+3y):y}{(6x-7y):y}$
$\to A=\dfrac{5\cdot \dfrac{x}{y}+3}{6\cdot \dfrac{x}{y}-7}$
$\to A=\dfrac{5\cdot\dfrac23+3}{6\cdot \dfrac23-7}$
$\to A=-\dfrac{19}{3}$
b.Ta có:
$\dfrac{x}{y}=\dfrac35\to x=\dfrac35y$
$\to B=\dfrac{\dfrac35y+y}{\dfrac35y-y}$
$\to B=\dfrac{\dfrac85y}{\dfrac{-2}5y}$
$\to B=-4$
c.Ta có:
$C=\dfrac1{5.7}+\dfrac1{7.9}=...+\dfrac{1}{63.65}$
$\to 2C=\dfrac2{5.7}+\dfrac2{7.9}=...+\dfrac{2}{63.65}$
$\to 2C=\dfrac{7-5}{5.7}+\dfrac{9-7}{7.9}+...+\dfrac{65-63}{63.65}$
$\to 2C=\dfrac15-\dfrac17+\dfrac17-\dfrac19+...+\dfrac1{63}-\dfrac1{65}$
$\to 2C=\dfrac15-\dfrac1{65}$
$\to 2C=\dfrac{12}{65}$
$\to C=\dfrac{6}{65}$
$\to$Số nghịch đảo là $\dfrac{65}{6}$
