Question

`((a^2+ax+x^2)/(ax+2ay)) ÷( (a^3−x^3)/(bx+2by))` ?

Answer 1

I tried this:

Explanation:

I would try changing the division into a mutiplication inverting the second fraction:
`(a^2+ax+x^2)/(ax+2ay)color(red)(xx((bx+2by)/(a^3-x^3))`
I would then try to rearrange collecting:
`(a^2+ax+x^2)/(acancel((x+2y)))xx(bcancel((x+2y)))/(a^3-x^3)`
`(a^2+ax+x^2)/(a)xx(b)/(a^3-x^3)`

we can write:
`a^3-x^3=(a-x)(a^2+ax+b^2)`
so we get:
`cancel(a^2+ax+x^2)/(a)xx(b)/((a-x)cancel(a^2+ax+b^2))=`
`=b/(a(a-x)`