Verified Answer :

meerkat18

#1. The problem ask to find the simplified form of the said equation, so in calculating it, you must first get is factored form and that is (x^2+9)(x^2-9)/x+3 then expand again, (x^2+9)(x+3)(x-3)/(x+3), then cancel the value and came up with an answer of (x^2+9)(x-3). 
#2 In getting its answer you must follow the rule of a^m/a^n = a^m-n and then you will get the answer of y^2z^2x^3. I hope this would help

Answer:

1. \((x^2+9)(x-3)\).

2.\(x^3y^2z^2\).

Step-by-step explanation:

1. The given expression is

\(\frac{x^4-81}{x+3}\)

\(\frac{(x^2)^2-(9)^2}{x+3}\)

\(\frac{(x^2+9)(x^2-9)}{x+3}\)          \([a^2-b^2=(a-b)(a+b)]\)

\(\frac{(x^2+9)(x^2-3^2)}{x+3}\)

\(\frac{(x^2+9)(x-3)(x+3)}{x+3}\)          \([a^2-b^2=(a-b)(a+b)]\)

\(\frac{x^4-81}{x+3}=(x^2+9)(x-3)\)

Therefore the simplified form of the given expression is \((x^2+9)(x-3)\).

2. The given expression is

\(\frac{(x^2yz)^2(xy^2z^2)}{(xyz)^2}\)

\(\frac{(x^4y^2z^2)(xy^2z^2)}{x^2y^2z^2}\)          \([(ab)^m=a^mb^m]\)

\(\frac{x^5y^4z^4}{x^2y^2z^2}\)           \([x^mx^n=x^{m+n}]\)

\(x^3y^2z^2\)          \([\frac{x^m}{x^n}=x^{m-n}]\)

Therefore the simplified form of the given expression is \(x^3y^2z^2\).