Question

How do you find the product of `9/(t-2)*((t+2)(t-2))/3`?

Answer 1

The final answer is 3(t+2) or 3t + 6 if you prefer.

Explanation:

You can cancel full binomials just like you can numerical values. So, the `t-2` term in the denominator of the first factor cancels the one in the numerator of the second factor.

`9/cancel(t-2) * ((t+2)cancel(t-2))/3`

Also, since 9 is 3 x 3, you can cancel the denominator of the second factor:

`(cancel9)color(red)3*(t+2)/cancel3 = 3(t+2)`

Answer 2

`3t+6`

Explanation:

`color(blue)"cancel common factors"` on the numerators/denominators of the fractions.

`rArrcolor(red)(9)/color(blue)((t-2))xx((t+2)color(blue)((t-2)))/color(red)(3)`

`=color(red)cancel(9)^3/(color(blue)cancel((t-2)^1))xx((t+2)color(blue)cancel((t-2)^1))/color(red)cancel(3)^1`

`=(3(t+2))/1`

`=3(t+2)`

`=3t+6`