1 Answer

BNL · Answer 1 · 2020-06-11T06:28:12+0000

I'll assume the question marks are due to some buggy code, and that the expression you're supposed to simplify is just

(x^2+9x+20)/(x+7)

We carry out the division algorithm:

Since
$x^2=x\cdot x$ , we can multiply
x+7 by
to get
x^2+7x . Then subtracting this from
x^2+9x+20 gives a remainder of

(x^2+9x+20)-(x^2+7x)=2x+20

Next, since
$2x=2\cdot x$ , we can multiply
x+7 by
to get
2x+14 , then subtracting this from the previous remainder gives a new remainder of

(2x+20)-(2x+14)=6

To summarize, we simplified the rational expression as

$(x^2+9x+20)/(x+7)=x+(2x+20)/(x+7)=x+2+\frac6{x+7}$

so that the quotient terms is
x+2 , and the remainder is
.

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