Question

simplify
(x+3)(x+7) divided by 3x+21

Answer 1

factor the denominator as \(3(x+7)\) and then so a tiny bit of cancellation

Answer 2

got it?

Answer 3

21x?

Answer 4

\[\frac{(x+3)(x+7)}{3(x+7)}\] is a start
now cancel

Answer 5

\[\frac{(x+3)\cancel{(x+7)}}{3\cancel{(x+7)}}\]

Answer 6

(x+3)(x+7) / 3x+21

x+3 evaluates to x+3
x+7 evaluates to x+7

Multiplying x+3 by x+7 is a classic Algebra problem. Here, you are trying
to multiply two binomials together (two expressions that each contain two terms).
Your book might call this finding the "Product of Two Binomials".

To work this problem, we'll use the "F.O.I.L." method. F.O.I.L. stands
for First, Outer, Inner, Last.

First, we'll multiply the two First terms, the x and x together.

Multiply x and x

Multiply the x and x

Multiply x and x


Combine the x and x by adding the exponents, and keeping the x, to get

The answer is



x × x =

Second, we'll multiply the two Outer terms, the x and 7 together.

Multiply x and 7

Multiply x and 1


The x just gets copied along.

The answer is x

x

x × 7 = 7x

Third, we'll multiply the two Inner terms, the 3 and x together.

Multiply 3 and x

Multiply 1 and x


The x just gets copied along.

x

3 × x = 3x

7x combines with 3x to give 10x

Lastly, we'll multiply the two Last terms, the 3 and 7 together.

Multiply 3 and 7


1

3 × 7 = 21

(x+3)*(x+7) evaluates to

Multiply x and 3

Multiply x and 1


The x just gets copied along.

The answer is x

x

3*x evaluates to 3x

To divide by 3x

divide each term in by 3x term by term.

To divide by x


Divide by x by subtracting the exponents, and keeping the x, to get x

The answer is x

÷ 3x =

To divide x by x


Divide x by x by subtracting the exponents, and keeping the x, to get 1

Why 1? since subtracting the exponents gives zero, the x completely drops out.This because anything (other than 0) to the 0th power is 1.

10x ÷ 3x =

To divide 1 by x


The x just gets copied along in the denominator.

The answer is

21 ÷ 3x =

(x+3)*(x+7)/3*x evaluates to

+ 21 =

The answer is

(x+3)*(x+7)/3*x+21 evaluates to

Answer 7

leading off from @satellite73
(x+3)(x+7)
---------- = ??
3(x+7)
the x+7 term gets cancelled
so you are left with x+3/3

Answer 8

3
____ = -7/
x+7

Answer 9

thanks guys!

Answer 10

i think maybe it is not clear
when you cancel you are left only with \(\frac{x+3}{3}\) as the common factor of \(x+7\) cancels top and bottom