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

1 Answer
Oct 1, 2017

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

Explanation:

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))