Question

Home -Executive Office of3 MemberConfidentiality Stat..Adapt Web Service3 New TabWrite equivalent rational expressions with the least common denominator.Like numerical fractions, you can write equivalent rational expressions with a least common denominator bymultiplying the numerator and denominator by the missing factor in the LCD.For the denominator (x + 2) to become the LCD (x + 2)(x - 7), it needs to be multiplied by (x - 7). Tomaintain an equivalent fraction, multiply the entire rational expression by a form of 1.x + 2X-7(x + 2)(x - 7)Similarly, for the denominator (x - 7) to become the LCD (x + 2)(x - 7), it needs to be multiplied by(x + 2). Again, to maintain an equivalent fraction, multiply the entire rational expression by a form of 1.x + 221(x + 2)(x-7)Thus, rewriting the given rational expressions in terms of their least common denominator gives the following

Answer 1

The given rational expression is,

`(7)/(x+2)`

The denominator of the expression becomes LCD (x+2)(x-7), multiply the numerator and denominator of the rational expression by (x-7).

`\begin{gathered} (7)/(x+2)=(7)/(x+2)((x-7)/(x-7)) \\ =(7(x-7))/((x+2)(x-7)) \end{gathered}`

In the rational expression 2/(x-7), the denominator (x-7) becomes the LCD (x+2)(x-7) if the numerator and denominator of the expression is multipied by (x+2).

`\begin{gathered} (2)/(x-7)=(2)/((x-7))((x+2)/(x+2)) \\ =(2(x+2))/((x+2)(x-7)) \end{gathered}`