# Homework Help: Simplifying an algebra question

1. Dec 31, 2012

### evosy1978

Hello,

Ive was reading my literature today and it showed me some algebra, which i did not understand how it went from one step to the next...

What was done to simplify
V= x^2 ( 75-x^2 / 2x ) into V= x/2 ( 75-x^2 )

& then what was done to simplify ^^^

V= x/2 ( 75-x^2 ) into V= 1/2 ( 75x-x^3 )

(for anyone interested the above has now been differentiated)

I would now like to know when finding x how they go from
1/2 ( 75-3x^2 ) = 0 to this 75 = 3x^2

Thanks for any help. I know I'm missing something simple here?

2. Dec 31, 2012

### HallsofIvy

You mean V= x^2((75- x^2)/(2x)). That is, the entire "75- x^2" is divided by 2x. You can factor 1/(2x) out to get (x^2/2x)(75- x^2)= (1/2)(x)(75- x^2).

Now multiply the "x" back into the 75- x^2: x/2= (1/2)(x)(75- x^2)= (1/2)(75(x)- x^2(x))= (1/2)(75x- x^3).

Multiply both sides by 2 to get 75- 3x^2= 0
then add 3x^2 to both sides: 75= 3x^2

Although you dont mention it, an obvious next thing to do is to divide both sides by 3:
25= x^2. What you do now depends upon what the question is! If it is to solve for x, take the square root of both sides.

3. Jan 1, 2013

### evosy1978

Ok, thanks for taking the time to reply, just to let you know it can sometimes take time for things to "click in my head" lol.. Im still confused, so can I break it down and show you where Im at...

I understand the last bit as you have cancelled out one of the x's from the top and bottom of the fraction.

Im confused as to where the part in red 1/(2x) came from?
I also dont understand why the 2x disappears from under the 75-x^2 and then appears under the x^2?

Thanks

Last edited: Jan 1, 2013
4. Jan 1, 2013

### MrWarlock616

It's like this:

$V= x^2 (\frac{75-x^2}{2x})=\frac{1}{2x}x^2(75-x^2)=\frac{x}{2}(75-x^2)$

5. Jan 1, 2013

### I like Serena

Here's a couple of the rules for working with fractions and multiplications:
$$\frac 2 3 = 2 \cdot \frac 1 3$$
$$2 \cdot 3 \cdot 4 = 4 \cdot 2 \cdot 3$$
$$\frac {3 \cdot 2} {5 \cdot 2} = \frac 3 5$$
These are the rules MrWarlock applied.