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Question
Simplify `(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
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Solution
2a2 + 5a + 3a + 3 = 2a2 + 2a + 3a + 3
= 2a(a + 1) + 3 (a + 1)
= (a + 1) (2a + 3)
2a2 + 7a + 6 = 2a2 + 3a + 4a + 6
= a(2a + 3) + 2 (2a + 3)
= (2a + 3) (a + 2)
a2 + 6a + 5 = (a + 5) + (a + 1)
– 5a2 – 35a – 50 = – 5(a2 + 7a + 10)
= – 5(a + 5)(a + 2)
`(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
= `(("a" + 1)(2"a" + 3))/((2"a" + 3)("a" + 2)) ÷ (("a" + 5)("a" + 1))/(-5("a" + 5)("a" + 2))`
= `(("a" + 1))/(("a" + 2)) ÷ (("a" + 1))/(-5("a" + 2))`
= `(("a" + 1))/(("a" + 2)) xx (-5("a" + 2))/(("a" + 1))`
= – 5
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