Add or Subtract. `(3x)/(x^2+3x-10) - 4/(x-2)`

1 Answer

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lemjay | High School Teacher | (Level 3) Senior Educator

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Since the two fractions have unlike denominators, determine the LCD.

To do so, factor the denominator of the first fraction.


Then, take the product of the different factors present in the denominators to get the LCD.
Since the different factors in the denominators are (x+5) and (x-2), then, the LCD is (x+5)(x-2).

So to express them with same denominators, multiply the second fraction by (x+5)/(x+5).



Now that they have same denominators, proceed to subtract the two fractions.






Hence,  `(3x)/(x^2+3x-10)-4/(x-2)=-(x+20)/((x+5)(x-2))` .