How do you simplify the expression #(3t^2-8t+4)/(6t^2-4t)#?

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Answer 1 · 2016-07-30T16:07:54

:#" "1/(2t)(t-2) = 1/2-1/t#

The first thing to try is to see if there are any common factors you can cancel out.

#color(blue)("Consider the numerator")#

3 is prime so I can not factor out any constants from all of the numerator

#color(blue)("Try 1:") ->(3t-1)(t-4) = 3t^2-12t-4t+4 color(red)(larr" Fail")#

#color(blue)("Try 2:") " Write as: "color(green)( 3t^2-6t-2t+4)color(purple)( -> 3t(t-2)-2(t-2))#
Giving: #" "(t-2)(3t-2)color(red)(" "larr" Works")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the denominator")#

Factor out #2t" giving "2t(3t-2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#(3t^2-8t_4)/(6t^2-4t) -= ((t-2)cancel((3t-2)))/(2tcancel((3t-2)))#

giving:#" "1/(2t)(t-2) = 1/2-1/t#