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

Question

Hazel Anglin · Accepted Answer

:#" "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#

Jace Anderson · Answer

undefined To simplify the expression (3t^2-8t+4)/(6t^2-4t), you can factor out a common term from both the numerator and denominator. In this case, the common term is t. Factoring out t, we get t(3t-8+4t)/(t(6t-4)). Simplifying further, we have (3t^2-8t+4t)/(6t^2-4t). Combining like terms in the numerator, we get (3t^2-4t)/(6t^2-4t). Now, we can cancel out the common term of t in the numerator and denominator, resulting in (3t-4)/(6t-4).

Eva Adamson · Answer

undefined To simplify the expression (3t^2 - 8t + 4) / (6t^2 - 4t), you can factor both the numerator and the denominator and then cancel out any common factors.

Factoring the numerator:
3t^2 - 8t + 4 can be factored into (3t - 2)(t - 2).

Factoring the denominator:
6t^2 - 4t can be factored into 2t(3t - 2).

Now, rewrite the expression with the factored forms:
[(3t - 2)(t - 2)] / [2t(3t - 2)].

Now, you can cancel out the common factor (3t - 2) from both the numerator and the denominator:
(t - 2) / (2t).

So, the simplified expression is (t - 2) / (2t).