Math Help - simply algeberic fraction

1. simply algeberic fraction

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

as a single fraction in its simplest form.

I got $\frac{4x+4}{3x^{3} + 9x^{2} + 9x -3}$ but thats not the correct answer, can someone show me hot to get to $\frac{4}{3(x-1)(3x+1)}$

thank you.

2. Originally Posted by Tweety
express $\frac{x+1}{3x^{2}-3} - \frac{1}{3x+1}$

as a single fraction in its simplest form.

I got $\frac{4x+4}{3x^{3} + 9x^{2} + 9x -3}$ but thats not the correct answer, can someone show me hot to get to $\frac{4}{3(x-1)(3x+1)}$

thank you.
hi

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

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

$\frac{4x+4}{3(x+1)(x-1)(3x+1)}$

what do u see in common for the numerator ?

hi

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

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

$\frac{4x+4}{3(x+1)(x-1)(3x+1)}$

what do u see in common for the numerator ?
Is that the correct answer? And is that the same as my answer but simplified?

4. Originally Posted by Tweety
Is that the correct answer? And is that the same as my answer but simplified?
its not fully simplified , i left the last step for you , note that 4x+4=4(x+1)

so when you cancel the x+1 , you will get the answer in your book