One approach is to recognize that we can SIMPLIFY the fraction \(\frac{a^2 - b^2}{(a - b)}\) by first factoring the numerator.

We get: \(|\frac{a^2 - b^2}{(a - b)}| = |\frac{(a+b)(a-b)}{(a - b)}|=|a+b|\)

So, a ★ b = |a + b|
This means: 4 ★ 2 = |4 + 2| = |6| = 6

Cheers,
Brent

Given that \(a ★ b = |\frac{(a^2 - b^2)}{(a - b)}|\) and we need to find the value of \(4 ★ 2\)

To find \(4 ★ 2\) we need to compare what is before and after ★ in \(4 ★ 2\) and a ★ b

=> We need to substitute a with 4 and b with 2 in a ★ b to get the value of \(4 ★ 2\)

=> \(4 ★ 2 = |\frac{(4^2 - 2^2)}{(4 - 2)}|\) = \(|\frac{16 - 4}{2}|\) = \(|\frac{12}{2}|\) = \(|6|\) = 6
( Watch this video to learn about the Basics of Absolute Value )

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters