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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

Respuesta :

The given rational expression is,

[tex]\frac{7}{x+2}[/tex]

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

[tex]\begin{gathered} \frac{7}{x+2}=\frac{7}{x+2}(\frac{x-7}{x-7}) \\ =\frac{7(x-7)}{(x+2)(x-7)} \end{gathered}[/tex]

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).

[tex]\begin{gathered} \frac{2}{x-7}=\frac{2}{(x-7)}(\frac{x+2}{x+2}) \\ =\frac{2(x+2)}{(x+2)(x-7)} \end{gathered}[/tex]

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