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Simplify and answer the boxes.

Simplify and answer the boxes.-example-1
User MacroMarc
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1 Answer

5 votes

Answer:


\huge\boxed{(x^2+9^2)/(x-3y)+(6xy)/(3y-x)=x-3y}

Explanation:

Domain:


x-3y\\eq0\Rightarrow x\\eq3y


(x^2+9y^2)/(x-3y)+(6xy)/(3y-x)=(x^2+9y^2)/(x-3y)+(6xy)/(-(x-3y))\\\\=(x^2+9y^2)/(x-3y)-(6xy)/(x-3y)=(x^2+9y^2-6xy)/(x-3y)\\\\=(x^2-2(x)(3y)+(3y)^2)/(3y-x)=((x-3y)^2)/(3y-x)\\\\=(\bigg[-1(3y-x)\bigg]^2)/(3y-x)=((-1)^2(3y-x)^2)/(3y-x)\\\\=(1(x-3y)(x-3y))/(x-3y)=x-3y

Used:

The distributive property: a(b + c) = ab + ac

(a - b)² = a² - 2ab + b²

User Kranthi Kumar
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