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# Find the Lcd of the rational expression. Also find the differnce of the rational expression in the simplest form.

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Find the Lcd of the rational expression. Also find the differnce of the rational expression in the simplest form.

7/y,21/x^2-y

Guest Feb 25, 2017
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Find:

(1) $$\text{LCD of }\dfrac{7}{y}\text{ and }\dfrac{21}{x^2-y}$$

and

(2) $$\dfrac{7}{y}-\dfrac{21}{x^2-y}$$

First question:

$$\text{LCD}(\dfrac{7}{y},\dfrac{21}{x^2-y})\\ =\text{LCM}(y,x^2-y)\\ =x^2y-y^2$$

Second question:

$$\dfrac{7}{y}-\dfrac{21}{x^2-y}\\ =\dfrac{7(x^2-y)}{x^2y-y^2}-\dfrac{21y}{x^2y-y^2}\\ =\dfrac{7x^2-7y-21y}{x^2y-y^2}\\ =\dfrac{7x^2-28y}{x^2y-y^2}$$

MaxWong  Feb 25, 2017