Question

How do you simplify `(x^2-16)/x^3+(x^3+1)/x^4`?

Answer 1

See a solution process below:

Explanation:

To add fractions they must be over a common denominator. We can multiply the fraction on the left by the appropriate form of `1` to give it a common denominator with the fraction on the right:

`(x/x xx (x^2 - 16)/x^3) + (x^3 + 1)/x^4 =>`

`(x(x^2 - 16))/(x xx x^3) + (x^3 + 1)/x^4 =>`

`((x xx x^2) - (x xx 16))/x^4 + (x^3 + 1)/x^4 =>`

`(x^3 - 16x)/x^4 + (x^3 + 1)/x^4`

We can now add the numerators of the two fractions over the common denominator:

`(x^3 - 16x + x^3 + 1)/x^4 =>`

`(x^3 + x^3 - 16x + 1)/x^4 =>`

`(1x^3 + 1x^3 - 16x + 1)/x^4 =>`

`((1 + 1)x^3 - 16x + 1)/x^4 =>`

`(2x^3 - 16x + 1)/x^4`