Multiplying Rational Expressions

[wScott]

This is a question I have to do for tomorrow

$$\frac{1+4x+4x^2}{x}\times\frac{3x^4}{12x^2-3}$$.

I just factor the tops and then cancel where I can. This is what I came up with:

$$\frac{3x^4}{12x^3-3x}$$

But the answer key says:

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

What have I done wrong?

 

[topsquark]

This is a question I have to do for tomorrow

$$\frac{1+4x+4x^2}{x}\times\frac{3x^4}{12x^2-3}$$.

I just factor the tops and then cancel where I can. This is what I came up with:

$$\frac{3x^4}{12x^3-3x}$$

But the answer key says:

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

What have I done wrong?

You aren't factoring carefully enough. You've got leftover factors floating around. Write out ALL of the steps!

$$\frac{1+4x+4x^2}{x}\times\frac{3x^4}{12x^2-3}$$

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

NOW do your cancelling.

-Dan

 

[wScott]

Ouch. That hurt my pride. I forget to factor the factor usually, that's going to kill me one day.

thanks for pointing out that pesky little mistake.

 

[topsquark]

Ouch. That hurt my pride. I forget to factor the factor usually, that's going to kill me one day.

thanks for pointing out that pesky little mistake.

Happens to the best of us. No worries, mate!

-Dan