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Question
Simplify `("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
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Solution
b2 + 3b – 28 = (b + 7) (b – 4)
b2 + 4b + 4 = (b + 2) (b + 2)
b2 – 49 = b2 – 72
= (b + 7) (b – 7)
b2 – 5b – 14 = (b – 7) (b + 2)
`("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
= `(("b" + 7)("b" - 4))/(("b" + 2)("b" + 2)) ÷ (("b" + 7)("b" - 7))/(("b" - 7)("b" + 2))`
= `(("b" + 7)("b" - 4))/(("b" + 2)("b" + 2)) xx (("b" + 2))/(("b" + 7))`
= `(("b" - 4))/(("b" + 2))`
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