If a + c b, then 4a² - (a + b - c)²/a-b+c=

The key to answering this question is recognizing that we have a difference of squares hiding in the given algebraic expression

We know this because \(4a^2\) can be re-written as \((2a)^2\), which means \(4a^2\) is a SQUARE.
Likewise, \((a + b - c)^2\) is obviously a SQUARE.

So the original expression can be re-written as: \(\frac{{(2a)^2 - (a + b - c)^2}}{{a - b + c}} =\)

We can factor a difference of squares as follows: \(x^2 - y^2 = (x + y)(x - y)\)

So, take: \(\frac{{(2a)^2 - (a + b - c)^2}}{{a - b + c}}\)

Factor the numerator to get: \(\frac{{[2a + (a + b - c)][2a - (a + b - c)]}}{{a - b + c}}\)

Simplify the numerator to get: \(\frac{{(3a + b - c)(a -b+c)}}{{a - b + c}}\)

Since we have \((a -b+c)\) in the numerator and denominator, they cancel out to get: \(3a + b - c\)

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