Short simple algebra problem: (4x^-2 + 5x^-1 + 1) / (4x^-1 + 1)

[Daniel56]

Hello, I have one problem I have been stuck on for sometime now. It is not a very tedious problem yet I can not get the right answer for it. the problem is (4x^-2+5x^-1+1)/(4x^-1+1). I thought you have to move the 4x^-2 and the 5x^-1 down to the bottom of the fraction in order to make them positive exponents, however, the correct answer is (x+1)/x.

If any one could give me some insight as to how I get there or where I went wrong please feel free to tell me .

Much appreciated! -Daniel

 

[Deleted member 4993]

Hello, I have one problem I have been stuck on for sometime now. It is not a very tedious problem yet I can not get the right answer for it. the problem is (4x^-2+5x^-1+1)/(4x^-1+1). I thought you have to move the 4x^-2 and the 5x^-1 down to the bottom of the fraction in order to make them positive exponents, however, the correct answer is (x+1)/x.

If any one could give me some insight as to how I get there or where I went wrong please feel free to tell me .

Much appreciated! -Daniel

Multiply the numerator and the denominator by x²/x² - to get

(4 + 5x + x²)/[x(4 + x)]

Now factorize the numerator and eliminate the common factor/s.