I got this wrong in a test. Now I'm sitting and puzzling. The initial fraction is what the answer key said, the last, mine.

 

What did I do wrong in: 2x/(1+4x) = (2x/x)/(1/x+4x/x) = 2/(1/x+4) = 2(x/1)+2(1/4) = 2x+1/2

 

When I substitute 10 for x, the answers are different. If there is a link or source, it would be very helpful too. Thanks!

I got this wrong in a test. Now I'm sitting and puzzling. The initial fraction is what the answer key said, the last, mine.

 

What did I do wrong in: 2x/(1+4x) = (2x/x)/(1/x+4x/x) = 2/(1/x+4) = 2(x/1)+2(1/4) = 2x+1/2

 

When I substitute 10 for x, the answers are different. If there is a link or source, it would be very helpful too. Thanks!

 

 

[math]2x/(1+4x) = (2x/x)/(1/x+4x/x) = 2/(1/x+4) \ne 2(x/1)+2(1/4) = 2x+1/2 [/math]

[math]2x/(1+4x) = (2x/x)/(1/x+4x/x) = 2/(1/x+4) \ne 2(x/1)+2(1/4) = 2x+1/2 [/math]

Thanks!

A trick to solving this is to multiply by 1: (1/x + 4)/(1/x + 4), then you have a way to split this equation into (2/x)/(1/x + 4)² and 8/(1/x + 4)²

A trick to solving this is to multiply by 1: (1/x + 4)/(1/x + 4), then you have a way to split this equation into (2/x)/(1/x + 4)² and 8/(1/x + 4)²

I don't understand why I should split it. I didn't need to simplify past the first fraction on the initial question. Dr Rocket answered my question perfectly.

 

I have another quick question: if you are finding the (sqrt of 2x)/(the sqrt of x), can you just cancel the x's and get sqrt of 2, x positive for an answer? And if the numerator was x squared, you'd have sqrt of x for your answer?

 

Thanks!

 

I have another question too. If the conjugate of a + b is a - b, is -a + b also a conjugate?

Edited August 23, 201114 yr by Brainteaserfan

Ah very well. That trick can sometimes simplify to the removal of the entire fraction. This was what I was aiming at but failed a bit with it: http://en.wikipedia.org/wiki/Conjugate_(algebra)

 

And yes, because you can split that into ((sqrt of 2)*(sqrt of x))/(sqrt of x) = sqrt of 2

I have another quick question: if you are finding the (sqrt of 2x)/(the sqrt of x), can you just cancel the x's and get sqrt of 2, x positive for an answer? And if the numerator was x squared, you'd have sqrt of x for your answer?

 

[math] \frac {\sqrt {2x}}{\sqrt x} = \frac {\sqrt 2 \sqrt x}{\sqrt x} = \sqrt 2 [/math]

 

I have another question too. If the conjugate of a + b is a - b, is -a + b also a conjugate?

 

[math] \overline {a + bi} = a-bi[/math] and [math] \overline {a+b} = a+b[/math] where [math]a,b \in \mathbb R[/math] and [math] i = \sqrt {-1}[/math]