Factoring Question: (9x + 36)/(3x + 9)

[freshmaker]

Hi,

My question is, when we are factoring equations, do we always need to expand the numerator.

eg

3(x+4)
------
(x+3)

should we expand to make it

3x + 12
--------
x+3

Thanks

 

[Otis]

My question is, when we are factoring equations, do we always need to expand the numerator.

eg

3(x+4)
------
(x+3)

should we expand to make it

3x + 12
--------
x+3

No -- when you report an answer, you don't need to expand factored expressions, unless you've been instructed to.

If you're working with ratios, then sometimes the numerators need to be expanded, in order to combine like-terms. Other times, we want to leave numerators and denominators in factored form, in order to see cancellations. It all depends upon the specific task.

If the example that you posted above is part of an exercise, can you post the entire exercise?

By the way, those algebraic ratios are "expressions", not "equations". An equation always contains an equals sign because an equation is a statement that two expressions are equal.

Cheers

 

[freshmaker]

No -- when you report an answer, you don't need to expand factored expressions, unless you've been instructed to.

If you're working with ratios, then sometimes the numerators need to be expanded, in order to combine like-terms. Other times, we want to leave numerators and denominators in factored form, in order to see cancellations. It all depends upon the specific task.

If the example that you posted above is part of an exercise, can you post the entire exercise?

By the way, those algebraic ratios are "expressions", not "equations". An equation always contains an equals sign because an equation is a statement that two expressions are equal.

Cheers

Cheers for that, I'm a 28 year old starting out on my mathematics journey after paying zero attention in school. I'll get there.

The question was to simplyfy

9x + 36
-------
3x + 9

the answer that was given had the numerator expanded rather than left in brackets, I was confused as to why.

 

[pka]

Cheers for that, I'm a 28 year old starting out on my mathematics journey after paying zero attention in school. I'll get there. The question was to simplyfy
9x + 36
-------
3x + 9
the answer that was given had the numerator expanded rather than left in brackets, I was confused as to why.

Note that numerator and denominator are multiples of three. So just divide. No need to factor.

 

[freshmaker]

Note that numerator and denominator are multiples of three. So just divide. No need to factor.

thanks.

It always seems so simple when someone points it out

 

[Otis]

It always seems so simple when someone points it out

If you didn't notice that the numerator and denominator are multiples of 3 (many beginning students don't), then factoring the top and bottom is what allows you to "see" that. Once you have factored enough expressions, experience allows you to begin skipping some factoring step(s). Either way, there's nothing wrong with factoring.

Here's a note, for future posts. If you type grouping symbols around the numerators and/or denominators in algebraic ratios, you can use a forward slash, instead of "drawing" a fraction bar, to show the ratio. (You won't be able to draw multiple ratios next to each other at this site because extra word spaces are deleted by the system. Also, if you go on to use mathematical software, you won't be able to input ratios by "drawing" them.)

The grouping symbols are used like this:

(9x + 36)/(3x + 9)

[3(3x + 12)]/[3(x + 3)]

The factored 3s may cancel because 3/3 = 1

(3x + 12)/(x + 3)

Since we're done, there's no need to factor the numerator (unless you've been instructed to).

 

[Steven G]

Hi,

My question is, when we are factoring equations, do we always need to expand the numerator.

eg

3(x+4)
------
(x+3)

should we expand to make it

3x + 12
--------
x+3

Thanks

If your objective is to factor you never multiple out--that is undoing factoring.

For example if you (x+2)(x-3)/(x-3) you see that the (x-3)'s cancels out. However if you multiplied the number you would get(x²-x-6)/(x-3) and you do not see anything canceling out. As Denis would say, Got it?