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

1 Answer
Mar 19, 2018

Answer:

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#