For each expression, write the equivalent expression where the denominator is the LCD.
The first thing we do is factor the expressions:
Neither of these expressions can be simplified, so now we need to find the LCD of
The LCD must contain the factors (x + 1) and (x – 1). Since the denominator of the second rational expression contains two copies of the factor (x – 1), the LCD must also contain two copies of the factor (x – 1). That's a lot of stuff, so hopefully it's got plenty of storage space.
The LCD is (x + 1)(x – 1)(x – 1).
To rewrite the rational expressions so that each has the LCD as its denominator, we multiply each expression by a clever form of 1. Better make it extra-clever. We think it may be on to us.