Rewrite rational expressions. Show all work and circle your answers.

Question

(4c^2-4c-8)/(c^4-4c^3+4c^2)  Thank you for your help.

Answer 1

  4c²-4c-8            4(c-2)(c+1)          4(c+1)

----------------  =  -----------------  =  ----------

c⁴-4c³+4c²           c²(c-2)(c-2)         c²(c-2)

Answer 2

factoring the terms

4(c^2-c-2)=4(c-2)(c+1)

c^4-4c^3+4c^2=c^2(c^2-4c+4)=c^2(c-2)(c-2)

4(c-2)(c+1)/c^2(c-2)(c-2)

cancel a (c-2) in the numerator and in the denominator

4(c+1)/c^2(c-2) is the simplest form