Reduce the following expression to lowest terms?

Question

(t^2 + t -6) / (3t^2 -27)

Thanks

Answer 1

(t^2+t-6)
=t^2+3t-2t-6
=t(t+3)-2(t+3)
=(t+3)(t-2)
3t^2-27
=3(t^2-9)
=3{(t)^2-(3)^2}
=3(t+3)(t-3)
Hence given expression
=(t+3)(t-2)/3(t+3)(t-3)
=(t-2)/3(t-3)

Answer 2

t^2 + t - 6
= (t + 3)(t - 2)

3t^2 - 27
= 3(t^2 - 9)
= 3(t - 3)(t + 3)

so...
(t + 3)(t - 2) / 3(t - 3)(t + 3)
= (t - 2) / 3(t - 3)

Answer 3

(t^2 + t -6) / (3t^2 -27)
= (t + 3)(t - 2) / 3(t -3)(t + 3)
= (t - 2) / 3(t - 3).

Answer 4

t^2+t-6=t^2-2t+3t-6
=t(t-2)+3(t-2)
=(t-2)(t+3)
3t^2-27=3(t^2-9)
=3{t^2-(3)^2}
=3(t-3)(t+3)
so we have
(t^2+t-6)/(3t^2-27)
=(t-2)(t+3)/3(t-3)(t+3)
=(t-2)/3(t-3) ans

Answer 5

x² - 2x – 3 -------------- 2x² - 8x + 6 (x – 3) (x + a million) => ---------------- (x – 3) (2x – 2) you could now cancel (x – 3) from the numerator and the denominator so we’r left with (x + a million) -------- 2(x – a million) that's the respond. The demanding area right here is splitting (x² - 2x – 3) into (x – 3) (x + a million) and likewise interior the denominator. Its in actuality factorizing a quadratic equation. I even have extra a link which elaborates somewhat yet on factorizing, yet there are a number of distinctive counsel on a thank you to do it

Answer 6

t^2 + t - 6 can be written as t + 3 and t -2

3t^2 - 27 can be written as 3(t^2 - 9) and that in turn can be written as 3(t + 3) (t - 3)

Thus the expression can be simplifed as

(t + 3) (t - 2) / 3(t + 3) (t - 3)

= (t - 2) / 3(t - 3)

Answer 7

(t-2)/3(t-3)

Oh well, just like the previous answer. The point to all these questions is that there is some common factor on the top and bottom that can be canceled. Just find it and you are pretty much done.

Answer 8

(t-2) / (3t-9)

Answer 9

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