The LCD of the rational expressions 7/5y^2+32y−64 and 10y/5y^2−18y+16 is (y + 8)(5y - 8)(y - 2)
The rational expressions are given as:
7/5y^2+32y−64 and 10y/5y^2−18y+16
Write out the denominators
5y^2+32y−64 and 5y^2−18y+16
Expand each of the denominator.
5y^2 + 32y - 64 = 5y^2 + 40y - 8y - 64
5y^2 − 18y + 16 = 5y^2 - 10y - 8y + 16
Factorize each of the denominator.
5y^2 + 32y - 64 = (5y - 8)(y + 8)
5y^2 − 18y + 16 = (5y- 8)(y - 2)
So, the factorized expression of the denominators are
(5y - 8)(y + 8) and (5y - 8)(y - 2)
Combine the expressions
(5y - 8)(y + 8)(5y - 8)(y - 2)
Remove repetition
(y + 8)(5y - 8)(y - 2)
Hence, the LCD of the rational expressions 7/5y^2+32y−64 and 10y/5y^2−18y+16 is (y + 8)(5y - 8)(y - 2)
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