Question

Multiply and simplify
x-1/x^2+2x+1 Multiplied by x^2-1/x+1

I don't understand and I need help ASAP!!

Answer 1

can you factor say -> \(\bf x^2+2x+1\) ?

Answer 2

wait, is the answer x+1/x-1 ? @jdoe0001

Answer 3

well... dunno what did you get for \(\bf x^2+2x+1\) ?

Answer 4

So, when your factoring that, it should add to 2 and multiply to one correct? @jdoe0001 I don't know if i'm factoring right

Answer 5

yes, keep in mind that \(\large \begin{array}{cccllll}
x^2&+2x&+1\\
&\uparrow &\uparrow \\
&1+1&1\cdot 1
\end{array}\)

Answer 6

okay, so now, where do I go from there, I have 1+1 and 1X1

Answer 7

@jdoe0001

Answer 8

well.. ok.. that means \(\large \begin{array}{cccllll}
x^2&+2x&+1\\
&\uparrow &\uparrow \\
&1+1&1\cdot 1
\end{array}\implies (x+1)(x+1)\)

Answer 9

if you FOIL the 2 binomials, you'd get the polynomial

Answer 10

(x-1)^2/(x+1)^2 correct? @jdoe0001

Answer 11

yeap \(\bf {\color{blue}{ a^2-b^2 = (a-b)(a+b)}}\\ \quad \\ \quad \\
\cfrac{x-1}{x^2+2x+1}\cdot \cfrac{x^2-1}{x+1}\implies \cfrac{x-1}{(x+1)(x+1)}\cdot \cfrac{{\color{blue}{ x^2-1}}}{x+1}\\ \quad \\

\cfrac{x-1}{(x+1)(x+1)}\cdot \cfrac{{\color{blue}{(x-1)(x+1)}}}{x+1}\implies \cfrac{(x-1)^2}{(x+1)^2}\)