# Thread: help with this problem

1. ## help with this problem

Hi, i was wondering if i simplify first or later on. If later, what step?

(x-5/2x)/(x^2/4x^2)

thank you for any help!

2. Hello,

It depends on what the question is

But generally, it's quite nice to simplify first

3. were just supposed to simplify..?

4. So why are you wondering ? oO

Can you show what you've done please ?

5. i've done nothing. i dont know where to start. can you help?

6. plz...:-D

7. Originally Posted by thefiz
Hi, i was wondering if i simplify first or later on. If later, what step?

(x-5/2x)/(x^2/4x^2)

thank you for any help!
$\frac{~~~~\frac{x-5}{2x}~~~~}{\frac{x^2}{4x^2}}$

The very first thing you should see is that the x^2 cancel out in the lower fraction.

$\frac{~~~~\frac{x-5}{2x}~~~~}{\frac{x^2}{4x^2}}~~~~=~~~~\frac{~~~~\f rac{x-5}{2x}~~~~}{\frac{1}{4}}$

Now, when you divide by a fraction, that is the same as multiplying by it's reciprocal. For example when you divide by 1/4, you are actually multiplying by 4/1.

$\frac{~~~~\frac{x-5}{2x}~~~~}{\frac{1}{4}}~~~~=~~~~\frac{x-5}{2x}*\frac{4}{1}$

Now Multiply the 4 through the numerator, and since anything times 1 equals 1, we can just ignore the 1

$\frac{x-5}{2x}*\frac{4}{1}~~~~=~~~~\frac{4(x-5)}{2x}$

And since we are multiplying by 4, and dividing by 2, 4/2 = 2 so we can simplify this:

$\frac{4(x-5)}{2x}~~~~=~~~~\frac{2(x-5)}{x}$

Now you can distribute the 2 if you like, or you can leave it factored like it is, that will depend on your teacher's preference. But when you distribute, you multiply the coefficient (the 2) by each element in the term (the x-5) so we get 2(x-5) = 2x-2*5 which is 2x-10

$\frac{2(x-5)}{x}~~~~=~~~~\frac{2x-10}{x}$

So there is your answer. You can choose whichever you think your instructor will consider "simpler"