Question

Simplify and answer the boxes.

Answer 1

`\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