## Task 3 - 050913

Compare the two numbers!

$$
A=\frac{5678901234}{6789012345} \quad \text { and } \quad B=\frac{5678901235}{6789012347}
$$
If we set the numerator of $A$ to $x$ and the denominator of $A$ to $y$, we obtain

$$
A=\frac{x}{y} \text { and } B=\frac{x+1}{y+2}
$$

and further

$$
A-B=\frac{x}{y}-\frac{x+1}{y+2}=\frac{x y+2 x-x y-y}{y(y+2)}=\frac{2 x-y}{y(y+2)}
$$

Since $2 x>y$, it follows that $2 x-y>0$ and, given $y>0$, we have $A-B>0$. Therefore, $A>B$.