Warm Up Solutions

Rewrite the fraction so that the denominator is $x^{2} - 1 given \frac{5 x}{x + 1}$ .

$x^{2} - 1 = (x + 1) (x - 1) \frac{5 x (x - 1)}{(x + 1) (x - 1)} \frac{5 x^{2} - 5 x}{x^{2} - 1}$

Note

Q: What kind of special product is $x^{2} - 1$ ?

A: The difference of two squares.

Rewrite the fraction so that the denominator is $10 x y given \frac{2 x - 3}{5 y}$ .

$\frac{2 x - 3}{5 y} (\frac{2 x}{2 x}) \frac{4 x^{2} - 6 x}{10 x y}$

Note

Q: Why should a 2 not be simplified out of the rational expression in this case?

A: Because then the denominator would not be 10xy.