How do you divide $x^2/(2x + 4 )$ ?

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Answer 1 · 2017-04-17T14:21:38

See below.

We have that

$x^2=q(x)(2x+4)+r(x)$

where $q(x)$ is the quocient, and $r(x)$ is the remainder

Analyzing the degrees involved we have:

$q(x) = ax+b$

$r(x) = c$

so

$x^2=2ax^2+2(b+2a)x+4b+c$

so we need

${(2a=1),(b+2a=0),(4b+c=0):}$

Solving for $a,b,c$ we have $a=1/2,b=-1,c=4$

and finally

$q(x)=x/2-1$

$r(x)=4$

How do you divide x^2/(2x + 4 )x^2/(2x + 4 )?