Question 322409
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First simplify things by multiplying each of the length and width expressions by 2 and then you only have to add two fractions.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(x)\ =\ \frac{16}{x\ -\ 9}\ +\ \frac{10}{x}]


Your denominators are coprime, which is to say that they have no factors in common, therefore the LCD is simply the product of the two denominators, to wit *[tex \Large x(x\ -\ 9)].  (It may be necessary, or simply aesthetic to multiply this out later on, but for now *[tex \Large x(x\ -\ 9)] is a perfectly good representation of your LCD.


Multiply the entire sum by 1 in the form of the LCD divided by the LCD:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(x)\ =\ \frac{16x}{x(x\ -\ 9)}\ +\ \frac{10(x\ -\ 9)}{x(x\ -\ 9)}\ =\ \frac{26x\ -\ 90}{x(x\ -\ 9)}]


Which can also be expressed as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(x)\ =\  \frac{26x\ -\ 90}{x^2\ -\ 9x}]


If you think that is prettier.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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