Question

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

Answer 1

Answer:

s⁴-6s³+12s²-10s+3

Step-by-step 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: $\bold{\dfrac{s^4-3s^3-2s+2}{(s-1)(s-1)(s-3)}}$

Step-by-step explanation:

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

  $\dfrac{s^3}{s^2-2s+1}+\dfrac{-2}{s^2-4s+3}$

$=\dfrac{s^3}{(s-1)(s-1)}+\dfrac{-2}{(s-1(s-3)}$

$=\dfrac{s^3}{(s-1)(s-1)}\bigg(\dfrac{s-3}{s-3}\bigg)+\dfrac{-2}{(s-1(s-3)}\bigg(\dfrac{s-1}{s-1}\bigg)$

$=\dfrac{s^4-3s^3-2s+2}{(s-1)(s-1)(s-3)}$