Please help me simplify these questions:
a - b - (a^2 / a+b)
(y^3 + 1) / (y^2 - 1) divided by (y^3 - y^2 + y) / (y^2 - 2y + 1)
And perhaps solve for 'y':
y^2 = 3y
2y^2 = y
y / y + 2 + 2 / y^2 - 4 = 1
$\displaystyle \frac{\frac{y^3 + 1}{y^2 - 1}}{\frac{y^3 - y^2 + y}{y^2 - 2y + 1}}$
First, let's get rid of those pesky fractions: Multiply the numerator and denominator by $\displaystyle (y^2 - 1)(y^2 - 2y + 1)$
$\displaystyle = \frac{\frac{y^3 + 1}{y^2 - 1}}{\frac{y^3 - y^2 + y}{y^2 - 2y + 1}} \cdot \frac{(y^2 - 1)(y^2 - 2y + 1)}{(y^2 - 1)(y^2 - 2y + 1)}$
(Pop quiz: Note that we only need to multiply by $\displaystyle (y - 1)^2(y + 1)$, why?)
$\displaystyle = \frac{(y^3 + 1)(y^2 - 2y + 1)}{(y^3 - y^2 + y)(y^2 - 1)}$
Now let's do some factoring:
$\displaystyle = \frac{[(y + 1)(y^2 - y + 1)][(y - 1)^2]}{[y(y^2 - y + 1)][(y + 1)(y - 1)]}$
Now let's do some(!) canceling:
$\displaystyle = y - 1;~y \neq -1, 1$
-Dan