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. |