Algebra - make the assumption?

[MathJakob]

$\frac{6-2x}{x^2-9}\times\frac{15+5x}{4x}$

$\frac{2(3-x)}{(x-3)(x+3)}\times\frac{5(3+x)}{4x}$

$\frac{3-x}{x-3}\times\frac{5}{2x}$

Now do I make the assumption that $x\neq3$ ?

If I make the assumption that $x\neq3$ then $-1\times\frac{5}{2x} = -\frac{5}{2x}$

 

[micromass]

$\frac{6-2x}{x^2-9}\times\frac{15+5x}{4x}$

$\frac{2(3-x)}{(x-3)(x+3)}\times\frac{5(3+x)}{4x}$

$\frac{3-x}{x-3}\times\frac{5}{2x}$

Now do I make the assumption that $x\neq3$ ?

If I make the assumption that $x\neq3$ then $-1\times\frac{5}{2x} = -\frac{5}{2x}$

You started of with

$$\frac{6-2x}{x^2-9}\times\frac{15+5x}{4x}$$

For this to be well-defined, you make the assumption there that $x\neq -3, 0, 3$. So you make the assumption in the beginning instead of in the end.

 

[MathJakob]

You started of with

$$\frac{6-2x}{x^2-9}\times\frac{15+5x}{4x}$$

For this to be well-defined, you make the assumption there that $x\neq -3, 0, 3$. So you make the assumption in the beginning instead of in the end.

How can you tell before even starting the question that $x\neq-3,0,3$ ? It only became obvious to me once I got to the last section. Even still my main question was is it the right thing to do to make the assumption? Should I be doing this with all questions and just include where $x\neq-3,0,3$ along with my answer?

Would an examiner be looking for these types of checks?

 

[micromass]

How can you tell before even starting the question that $x\neq-3,0,3$ ?

You want to avoid dividing by $0$. So the denominator shouldn't be $0$. I see two denominators, namely $x^2 - 9$ and $4x$. Neither should be $0$. Now, solving things, we get that $x^2 - 9 = 0$ if and only if $x=-3,3$ and $4x = 0$ if and only if $x=0$. So you don't want $x=-3,0,3$.

It only became obvious to me once I got to the last section. Even still my main question was is it the right thing to do to make the assumption?

Yes, you should make the assumption. But you should make the assumption in the beginning.

Should I be doing this with all questions and just include where $x\neq-3,0,3$ along with my answer?

Yes.

Would an examiner be looking for these types of checks?

They should be looking out for these things.

 

[MathJakob]

Ok thank you