Final answer:
The expression (k^(2)-36)/(48-2k-k^(2))*(k+8)/(k-3) simplifies to -(k-6)*(k+8)/[(k-8)*(k-3)]
Step-by-step explanation:
To simplify the given expression, we first factorise the terms in the numerator and denominator. We factorise k^(2)-36 as (k+6)(k-6) and 48-2k-k^(2) as -(k+6)(k-8). The expression then becomes (k+6)(k-6)/-(k+6)(k-8)*(k+8)/(k-3).
Looking at the expression, we can see that the term (k+6) exists in both the numerator and the denominator, so we can cancel those out. The simplified version of the equation then becomes -(k-6)/(k-8)*(k+8)/(k-3).
Now, we can further simplify this by combining the fractions, which gives us -(k-6)*(k+8)/[(k-8)*(k-3)].
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