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# algebra question

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How do I simplify this expression?

Sep 7, 2020

#1
+141
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Daunting.

$$\frac{\frac{a^2}{x-a}+\frac{b^2}{x-b}+\frac{c^2}{x-c}+a+b+c}{\frac{a}{x-a}+\frac{b}{x-b}+\frac{c}{x-c}}=\frac{a+b+c}{\frac{a}{x-a}+\frac{b}{x-b}+\frac{c}{x-c}}+a+b+c=\frac{a+b+c}{\frac{a(x-b)(x-c)+b(x-a)(x-c)+c(x-a)(x-b)}{(x-a)(x-b)(x-c)}}+a+b+c$$

Sep 8, 2020
#2
0

From the top line,

$$\displaystyle \frac{a^{2}}{(x-a)}+a=\frac{a^{2}+a(x-a)}{(x-a)}=\frac{ax}{(x-a)}.$$

Similarly,

$$\displaystyle \frac{b^{2}}{(x-b)}+b=\frac{bx}{(x-b)}\quad \text{and} \quad \frac{c^{2}}{(x-c)}+c=\frac{cx}{(x-c)}.$$

Now put those together, remove the x as a common factor and then cancel.

Result is simply x.

Sep 8, 2020