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

1 Answer
Mar 19, 2018

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