# Algebra - make the assumption?

1. Jul 28, 2013

### 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 $-1\times\frac{5}{2x} = -\frac{5}{2x}$

2. Jul 28, 2013

### micromass

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.

3. Jul 28, 2013

### MathJakob

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?

4. Jul 28, 2013

### micromass

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 $x=-3,0,3$.

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

Yes.

They should be looking out for these things.

5. Jul 28, 2013

Ok thank you