Question

How do you find the product of `t^2/((t-4)(t+4))*(t-4)/(6t)`?

Answer 1

See a solution process below:

Explanation:

First, cancel common terms in the numerator and denominator:

`t^color(red)(cancel(color(black)(2)))/(color(blue)(cancel(color(black)((y - 4))))(t + 4)) * color(blue)(cancel(color(black)(t - 4)))/(6color(red)(cancel(color(black)(t)))) =>`

`t/(t + 4) * 1/6 =>`

`(t * 1)/((t + 4)6) =>`

`t/((6 * t) + (6 * 4)) =>`

`t/(6t + 24)`

However, because we cannot divide by `0` in the original equation we must exclude some values for `t`:

• `t - 4 = 0` means `t != 4`

• `t + 4 = 0` means `t != -4`

• `6t = 0` means `t != 0`

Therefore:

`t/(6t + 24)` where `t != 4` and `t != -4` and `t != 0`