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Question
Simplify `(12"t"^2 - 22"t" + 8)/(3"t") ÷ (3"t"^2 + 2"t" - 8)/(2"t"^2 + 4"t")`
Solution
12t2 – 22t + 8 = 2(6t2 – 11t + 4)
= 2[6t2 – 8t – 3t + 4]
= 2[2t (3t – 4) – 1 (3t – 4)]
= 2(3t – 4) (2t – 1)
3t2 + 2t – 8 = 3t2 + 6t – 4t – 8
= 3t(t + 2) – 4(t + 2)
= (t + 2) (3t – 4)
2t2 + 4t = 2t(t + 2)
`(12"t"^2 - 22"t" + 8)/(3"t") ÷ (3"t"^2 + 2"t" - 8)/(2"t"^2 + 4"t")`
= `(2(3"t" - 4)(2"t" - 1))/(3"t") ÷ ("t" + 2) ((3"t" - 4))/(2"t"("t" + 2))`
= `(2(3"t" - 4)(2"t" - 1))/(3"t") ÷ ((3"t" - 4))/(2"t")`
= `(4(2"t" - 1))/3`
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