Epsilon Delta Limit Proof help!

lim x-> 6 (2x + 4) ^ 0.5 = 4

and

lim x-> -1 (-4x + 6) / (-3x + 2) = 2

help please im stuck on both proofs >_<

1) Note that |√(2x + 4) - 4|
= |√(2x + 4) - 4| * |√(2x + 4) + 4| / |√(2x + 4) + 4|, via conjugates
= |(2x + 4) - 16| / [√(2x + 4) + 4]
= 2|x - 6| / [√(2x + 4) + 4]
≤ 2|x - 6| / (0 + 4)
= (1/2) |x - 6|.

So given ε > 0, let δ = 2ε.
Then, 0 < |x - 6| < δ ==> |√(2x + 4) - 4| ≤ (1/2) |x - 6| < (1/2)(2ε) = ε, as required.
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2) This one is trickier.

Note that |(-4x + 6)/(-3x + 2) - 2|
= |(4x - 6)/(3x - 2) - 2|
= |[(4x - 6) - 2(3x - 2)]/(3x - 2)|
= 2 |x + 1| / |3x - 2|.

To bound the denominator, assume that |x + 1| < 1.
So, -1 < x + 1 < 1
==> -2 < x < 0
==> -6 < 3x < 0
==> -8 < 3x - 2 < -2
==> |3x - 2| > 2.

Hence, |(-4x + 6)/(-3x + 2) - 2| = 2 |x + 1| / |3x - 2| < 2|x + 1| * (1/2) = |x + 1|.

So given ε > 0, let δ = min {1, ε}.
Then, 0 < |x - (-1)| < δ ==> |(-4x + 6)/(-3x + 2) - 2| < |x + 1| < ε, as required.
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I hope this helps!