Factoring (x-17)/(x+2) + (13)/(6)

Amster

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Jan 6, 2010
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I don't understand how (x-17)/(x+2) + 13/6 becomes 19 (x-4)/6(x+2) when factoring. Can someone please explain?
 
It's just algebra.

x17x+2+136\displaystyle \frac{x-17}{x+2}+\frac{13}{6}

This is finding a common denominator. Same as adding fractions.

66(x17)(x+2)+136(x+2)(x+2)\displaystyle \frac{6}{6}\cdot \frac{(x-17)}{(x+2)}+\frac{13}{6}\cdot\frac{(x+2)}{(x+2)}

Now, we have a common denominator:

6(x17)+13(x+2)6(x+2)\displaystyle \frac{6(x-17)+13(x+2)}{6(x+2)}

19x766(x+2)\displaystyle \frac{19x-76}{6(x+2)}

Factor 19 out of the top:

19(x4)6(x+2)\displaystyle \frac{19(x-4)}{6(x+2)}
 
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