Question

What is the sum 3/x^2-g + 5/x+3

Answer 1

Answer: Choice D)
`(5x-12)/((x+3)(x-3))`

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Work Shown:

`(3)/(x^2-9) + (5)/(x+3)\\\\(3)/(x^2-9) + (5(x-3))/((x+3)(x-3))\\\\(3)/(x^2-9) + (5x-15)/(x^2-9)\\\\(3+5x-15)/(x^2-9)\\\\(5x-12)/(x^2-9)\\\\(5x-12)/((x+3)(x-3))\\\\`

The idea is to get the denominators to be the same to the LCD (lowest common denominator). Note in step 2, I multiplied top and bottom by (x-3) to get this done. Then in step 3, I used the difference of squares rule to get x^2-9. Afterward, we can combine the fractions and like terms.