Simplify the following expression:

$\frac{{(525+175)}^2-{(525-175)}^2}{(525\times 175)}$

The correct option is 4.

To simplify the given expression, we can identify a algebraic pattern in the numerator. Let's define:
$a=525$
and
$b=175$

Substituting $a$ and $b$ into the expression, we get:
$\frac{{(a+b)}^2-{(a-b)}^2}{a\times b}$

Now, let's expand the terms in the numerator using the standard algebraic identities:
${(a+b)}^2=a^2+2ab+b^2$
${(a-b)}^2=a^2-2ab+b^2$

Subtracting the second identity from the first:
${(a+b)}^2-{(a-b)}^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)$
${(a+b)}^2-{(a-b)}^2=a^2+2ab+b^2-a^2+2ab-b^2$
${(a+b)}^2-{(a-b)}^2=4ab$

Now, substitute this simplified numerator back into our fraction:
$\frac{4ab}{ab}$

Since $a\ne 0$ and $b\ne 0$, we can cancel out the term $ab$ from both the numerator and the denominator:
$\frac{4\cancel{ab}}{\cancel{ab}}=4$

Thus, the expression simplifies to the constant value of 4, regardless of the values of 525 and 175.