40. Five mark exercise problem X

If $A$ $=$ $\frac{x}{x + 1}$ and $B$ $=$ $\frac{1}{x + 1}$, then prove that $\frac{(A + B)^2 + (A - B)^2}{A \div B}$ $=$ $\frac{2(x^2 + 1)}{x (x + 1)^2}$.

 

Answer:

 

$(A + B)^2$ $=$

 

$(A - B)^2$ $=$

 

$A \div B$ $=$

 

$\frac{(A + B)^2 + (A - B)^2}{A \div B}$  $\frac{2(x^2 + 1)}{x (x + 1)^2}$