Simplify Completely: x + 4 sqrt (x-1) - 13/ x - 5

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Please help, im having alot of trouble with this problem.

Let y = √(x−1)
then y² = x − 1
and x = y² + 1

(x + 4√(x−1) − 13) / (x − 5)
= (y² + 1 + 4y − 13) / (y² + 1 − 5)
= (y² + 4y − 12) / (y² − 4)
= (y − 2)(y + 6) / ((y − 2)(y + 2))
= (y + 6) / (y + 2)
= (√(x−1) + 6) / (√(x−1) + 2)