Question

Plz can anyone tell me ninth question

Answer 1

9.simplify the following rational expressions in the lowest terms. Is this what you asked?

Answer 2

Given (ax^2 -x^3/a^3 + x^3   *   a^2 - ax+x^2/a^2x^2 + a^4) + a^2 - 2ax + x^2/a^4-x^4.   ----- (1)


1st Part : 

 = ax^2 - x^3/a^3 + x^3 * a^2 - ax + x^2/(a^2x^2 + a^4) can be written as

= (ax^2 - x^3)(a^2-ax+x^2)/(a^3+x^3)(a^2x^2+x^4)

= x^2(a-x)(a^2-ax+x^2)/(x^2(a^3+x^3)(a^2+x^2)

= (a-x)(a^2-ax+x^2)/(a+x)((a^2+x^2)(a^2-ax+x^2)

= (a-x)/(a-x)(a^2+x^2)   ----- (2)



2nd Part : 

a^2 - 2ax + x^2/a^4 - x^4 can be written as

= (x-a)^2/a^4-x^4.

= (x-a)(x-a)/(a+x)(a-x)(a^2+x^2)

= - (x-a/(a+x)(x^2+a^2).    ---- (3).


Substitute (2) and (3) in (1).

= a - x/(a+x)(a^2+x^2) - (x-a)/(a+x)(a^2+x^2)

= 2a - 2x/(a+x)(a^2+x^2).


Hope this helps!