Simplifying expressions

**lemontea** · May 11th 2008, 09:23 PM

1)Simplify for x>0
sqrt(x^4-4x^2)/x

i have tried
sqrt((x+2)(x-2))
sqrt x^2-4

but they are incorrect, can anyone help me?

2) rationalize the denominator and simplify
x-4/sqrt(x)-4

**Reckoner** · May 11th 2008, 09:46 PM

Hi lemontea.

Originally Posted by lemontea

1)Simplify for x>0
sqrt(x^4-4x^2)/x

i have tried
sqrt((x+2)(x-2))
sqrt x^2-4

but they are incorrect, can anyone help me?

When factoring, you left out an $x^2$ (Edit: No you didn't; you just canceled it--I'm too tired to read properly). It should be:

$\frac{\sqrt{x^4 - 4x^2}}x$

$=\frac{\sqrt{x^2\left(x^2 - 4\right)}}x$

Now, remember that $\sqrt{ab} = \sqrt{a}\sqrt{b}$ , and that $\sqrt{a^2} = |a|$ , and you should be able to simplify this.

Originally Posted by lemontea

2) rationalize the denominator and simplify
x-4/sqrt(x)-4

I am assuming you mean $\frac{x - 4}{\sqrt{x} - 4}$ and not $x - \frac4{\sqrt{x}} - 4$ as it is written. If so, please be more careful about your notation in the future.

Anyway, when rationalizing a binomial denominator, multiply the numerator and denominator of the fraction by the conjugate binomial. For example:

$\frac{a}{\sqrt{2} + \sqrt{3}}$

$=\frac{a\color{red}\,\left(\sqrt{2} - \sqrt{3}\right)}{\left(\sqrt{2} + \sqrt{3}\right)\color{red}\left(\sqrt{2} - \sqrt{3}\right)}$

$=\frac{a\,\sqrt{2} - a\,\sqrt{3}}{\left(\sqrt{2}\right)^2 + \sqrt{2}\,\sqrt{3} - \sqrt{2}\,\sqrt{3} - \left(\sqrt{3}\right)^2}$

$=\frac{a\,\sqrt{2} - a\,\sqrt{3}}{2 - 3}$

$=\frac{a\,\sqrt{2} - a\,\sqrt{3}}{-1}$

$=a\,\sqrt{3} - a\,\sqrt{2}$

**lemontea** · May 11th 2008, 11:30 PM

1.) I still cant seem to get this question. This is what I did
sqrt(x^4-4x^2)/x
=(sqrtx^2(x^2-4))/x
=(sqrt (x-2)(x+2))

2.) This is what i got for the
(sqrt(m)+4)(m-4)/m-16
but when i submitted it, it's incorrect. What did i do wrong?

**Reckoner** · May 11th 2008, 11:44 PM

Originally Posted by lemontea

1.) I still cant seem to get this question. This is what I did
sqrt(x^4-4x^2)/x
=(sqrtx^2(x^2-4))/x
=(sqrt (x-2)(x+2))

I misread your first post. The answers you got seem correct to me. Have you tried separating the radical into $\sqrt{x - 2}\sqrt{x + 2}$ ? I don't see what else you could do here.

Originally Posted by lemontea

2.) This is what i got for the
(sqrt(m)+4)(m-4)/m-16
but when i submitted it, it's incorrect. What did i do wrong?

Have you tried multiplying out the numerator? It sounds like you are trying to submit these to an online system, and it is probably very finicky about how your answers are formatted.

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