How do you simplify #\frac { t ^ { 2} - 2t } { t ^ { 4} - 16}#?

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Answer 1 · 2017-10-01T19:55:11

#t/((t+2)(t^2+4))#

To simplify algebraic fraction you need of factorise the top and bottom as much as you can and then cancel terms.

We can factorise the top by taking out a factor of #t# from both terms.

#(t(t-2))/(t^4-16)#

The bottom is a difference of two squares.

#(t(t-2))/((t^2-4)(t^2+4))#

The #t^2-4# is another difference of two squares.

#(t(t-2))/((t-2)(t+2)(t^2+4))#

We can now cancel terms.

#(tcancel((t-2)))/(cancel((t-2))(t+2)(t^2+4))#

#t/((t+2)(t^2+4))#