Question

Find the least common denominator for these two rational expressions s^3/s^2-2s+1 -2/s^2-4s+3

Answer 1

s⁴-6s³+12s²-10s+3

Explanation:

s³/(s²-2s+1) - 2/(s²-4s+3)

The denominators are (s²-2s+1) and (s²-4s+3). Since one is not a multiple of the other, the least common denominator will be their product.

(s²-2s+1)(s²-4s+3) = s⁴-4s³+3s²-2s³+8s²-6s+s²-4s+3

= s₄ +(-4s³-2s³)+(+3s²+8s²+s²)+(-6s-4s)+3

= s⁴-6s³+12s²-10s+3

Answer 2

Answer:
`\bold{(s^4-3s^3-2s+2)/((s-1)(s-1)(s-3))}`

Explanation:

Factor both denominators to see which factors are missing from each denominator. Then multiply both fractions so they have the same LCD.

`(s^3)/(s^2-2s+1)+(-2)/(s^2-4s+3)`

`=(s^3)/((s-1)(s-1))+(-2)/((s-1(s-3))`

`=(s^3)/((s-1)(s-1))\bigg((s-3)/(s-3)\bigg)+(-2)/((s-1(s-3))\bigg((s-1)/(s-1)\bigg)`

`=(s^4-3s^3-2s+2)/((s-1)(s-1)(s-3))`