# Thread: Simplifying expressions - algebra 2

1. ## Simplifying expressions - algebra 2

1) (x^3 - x^2 - 4x + 4)/ (x^3 - 4x)?

The answer is supposed to be x-1/x, how do I get there

I simplify it and all I get to is x^3 - (x-2)/ x(x+2).....anyone give me some help????

2) [1-h(k^-1)]/[ (h^-1) - (k^-1)]

1 minus h times k to the -1 divided/over h to the -1 minus k to the -1

The answer is supposed to be h..how do I get there? I'm clueless on this one. My fractions get all mixed up and stuff, I get confused on negative exponents...

2. Originally Posted by Dunit0001
1) (x^3 - x^2 - 4x + 4)/ (x^3 - 4x)?

The answer is supposed to be x-1/x, how do I get there

I simplify it and all I get to is x^3 - (x-2)/ x(x+2).....anyone give me some help????

2) [1-h(k^-1)]/[ (h^-1) - (k^-1)]

1 minus h times k to the -1 divided/over h to the -1 minus k to the -1

The answer is supposed to be h..how do I get there? I'm clueless on this one. My fractions get all mixed up and stuff, I get confused on negative exponents...
1)
$\frac{x^3 - x^2 - 4x + 4}{x^3 - 4x} = \frac{(x^3 - 4x) - (x^2 - 4)}{x(x^2 - 4)}$

so, can you continue now?

2)
$\frac{1 -hk^{-1}}{h^{-1} - k^{-1}} = \frac{1 - \frac{h}{k}}{\frac{1}{h} - \frac{1}{k}} = \frac{\frac{k - h}{k}}{\frac{k - h}{hk}}$

continue it.. Ü

3. Originally Posted by Dunit0001
1) (x^3 - x^2 - 4x + 4)/ (x^3 - 4x)?

The answer is supposed to be x-1/x, how do I get there

I simplify it and all I get to is x^3 - (x-2)/ x(x+2).....anyone give me some help????

2) [1-h(k^-1)]/[ (h^-1) - (k^-1)]

1 minus h times k to the -1 divided/over h to the -1 minus k to the -1

The answer is supposed to be h..how do I get there? I'm clueless on this one. My fractions get all mixed up and stuff, I get confused on negative exponents...
$\frac{x^{3}-x^{2}-4x+4}{x^{3}-4x}$

First lets factor the denominator, you can see that both terms have a common factor of x, so lets factor that out.

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

Now, you should be able to see that we could further factor it to x(x-2)(x+2), but lets first see what we can do with it like it is.

Do you see any common factors in the numerator? It's a bit subtle, but if you look for it you can see that $x^{3}-x^{2} = x^{2}(x-1)$ and also $-4x+4= -4(x-1)$

So you can rewrite the numerator as $x^{3}-x^{2}-4x+4=x^{2}(x-1) -4(x-1)$

Now, each of these terms has a common factor of (x-1) so lets factor that out. $x^{2}(x-1) -4(x-1) = (x-1)(x^{2}-4)$

Now lets replace our old unfactored numerator with our new factored numerator.

$\frac{x^{3}-x^{2}-4x+4}{x(x^{2}-4)}=\frac{(x-1)(x^{2}-4)}{x(x^{2}-4)}$

Now you can see that $(x^{2}-4)$ is in both the numerator and denominator, so they cancel eachother out.
$\frac{(x-1)(x^{2}-4)}{x(x^{2}-4)}=\frac{(x-1)}{x}$

This can be split up as follows
$\frac{(x-1)}{x}=\frac{x}{x}-\frac{1}{x}$

Which simplifies to
$\frac{x}{x}-\frac{1}{x}=1-\frac{1}{x}$