why does the the sign flip here when multiplying the denominator

[jolly vector]

I get the idea why it does this, but I don't get why it flips the sign of -3 to +3. (p.s I use Photomath as a learning tool not to cheat 😭)

[jolly vector]

also sry for wording it weirdly 💀

[rigid shoal]

Its because you are using difference of 2 squares. ,tex $a^2 - b^2 = (a + b)(a - b)$

[dense coral]

ymme

[rigid shoal]

,tex $ a = \sqrt{x+1} $
b = 3

[lapis patrol]

ur multiplying it by the conjugate

[dense coral]

ymme

[rigid shoal]

sorry, texit is new to me

a^ 2= x + 1 and b^2 = 9

a^ 2 - b^2 = x + 1 - 9 = x -8

[solar crater]

The goal is to take the radical out of the denominator

the sign flip is derived from the difference of squares factoring