Advertisements
Advertisements
Question
Simplify `(12"t"^2 - 22"t" + 8)/(3"t") ÷ (3"t"^2 + 2"t" - 8)/(2"t"^2 + 4"t")`
Advertisements
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`
APPEARS IN
RELATED QUESTIONS
Reduce the following rational expression to its lowest form
`(x^2 - 1)/(x^2 + x)`
Reduce the following rational expression to its lowest form
`(x^2 - 11x + 18)/(x^2 - 4x + 4)`
Reduce the following rational expression to its lowest form
`(9x^2 + 81x)/(x^3 + 8x^2 - 9x)`
Simplify `(4x^2y)/(2z^2) xx (6xz^3)/(20y^4)`
Simplify `(x + 2)/(4"y") ÷ (x^2 - x - 6)/(12y^2)`
Simplify `(x(x + 1))/(x - 2) + (x(1 - x))/(x - 2)`
If A = `x/(x + 1)` B = `1/(x + 1)` prove that `(("A" + "B")^2 + ("A" - "B")^2)/("A" + "B") = (2(x^2 + 1))/(x(x + 1)^2`
`(3y - 3)/y ÷ (7y - 7)/(3y^2)` is
Solve `1/3` (x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)
In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number
