how to solve attached

Question

how to solve this equation:

http://assets.openstudy.com/updates/attachments/553fc131e4b09cdd472aed61-nickymail48-1430241604611-jjm.png

Answer 1

For this problem, your goal is probably to combine those two fractions into one fraction. First, factor the denominators:

 

(x + 2) / ((x + 6)(x - 6)) - (2x) / ((x + 6)(x + 3))

 

Now, you'll want to find a common denominator. It's just a combination of every factor that appears in the first denominator ((x+6) and (x-6)) with everything you don't already have from the second denominator (just (x+3), since you already have (x+6)). So, your common denominator is (x+6)(x-6)(x+3). Multiply the first fraction by (x+3)/(x+3) and the second by (x-6)/(x-6) so they both wind up with the common denominator:

 

((x+2)(x+3)) / ((x+6)(x-6)(x+3)) - ((2x)(x-6)) / ((x+6)(x-6)(x+3))

 

Now that the denominators are the same, subtract the numerators and simplify by foiling and combining like terms:

 

((x+2)(x+3) - (2x)(x-6)) / ((x+6)(x-6)(x+3))

(x² + 3x + 2x + 6 - (2x² + 12x)) / ((x+6)(x-6)(x+3))

(x² + 5x + 6 - 2x² - 12x) / ((x+6)(x-6)(x+3))

(-x² - 7x + 6) / ((x+6)(x-6)(x+3))

 

This is your final answer.