simplify the fractional expression

**cm3pyro** · February 6th 2008, 09:35 PM

I can't seem to get the correct answer for this question..

**earboth** · February 7th 2008, 12:29 AM

Originally Posted by cm3pyro

I can't seem to get the correct answer for this question..

I'll show you step by step what I've done:

$\sqrt{1+\left(x^3-\frac1{4x^3}\right)^2} = \sqrt{1+\frac{(4x^6-1)^2}{16x^6}} = \frac1{4x^3} \cdot \sqrt{16x^6+(4x^6-1)^2}$ $= \frac1{4x^3} \cdot \sqrt{16x^6+16x^{12} - 8x^6 + 1} = \frac1{4x^3} \cdot \sqrt{16x^{12} + 8x^6 + 1} = \frac1{4x^3} \cdot \sqrt{(4x^6+1)^2} =$

$\boxed{\frac{4x^6+1}{4x^3}}$

**cm3pyro** · February 7th 2008, 04:53 AM

That's the answer that i got too, but according to my teacher, it's wrong.

**wingless** · February 7th 2008, 05:18 AM

Originally Posted by earboth

I'll show you step by step what I've done:

$\sqrt{1+\left(x^3-\frac1{4x^3}\right)^2} = \sqrt{1+\frac{(4x^6-1)^2}{16x^6}} = \frac1{4x^3} \cdot \sqrt{16x^6+(4x^6-1)^2}$ $= \frac1{4x^3} \cdot \sqrt{16x^6+16x^{12} - 8x^6 + 1} = \frac1{4x^3} \cdot \sqrt{16x^{12} + 8x^6 + 1} = \frac1{4x^3} \cdot \sqrt{(4x^6+1)^2} =$

$\boxed{\frac{4x^6+1}{4x^3}}$

The most common mistake in algebra calculations, $\sqrt{x^2} \neq x$ , $\sqrt{x^2} = |x|$ !

So you're right until $\frac{\sqrt{(4x^6+1)^2}}{\sqrt{(4x^3)^2}}$

It should be
$\frac{|4x^6+1|}{|4x^3|} = \left | \frac{4x^6+1}{4x^3} \right |$

Thread: simplify the fractional expression

LinkBack

Thread Tools

Display

simplify the fractional expression

Similar Math Help Forum Discussions

Simplify Rational Expression with Fractional Exponents

Simplify an expression involving fractional exponents by factoring

Simple problem... rearranging fractional exponent expression

Simplify this equation w/ fractional expnents

simplify the expression #2

Search Tags