2x+3/x^2+8x+15 (minus) x-7/x^2+2x-15?

Question

2x+3/x^2+8x+15 (minus) x-7/x^2+2x-15

Can someone please help me out, I need to know how to solve this problem. I am trying to study for a placement test, I already have the answer I just need to know how to get it. Thanks so much!

Answer 1

First, get the least common denominator...

{ 2x+3 / (x+3) (x+5) } - { x-7 / (x-3) (x+5) }

LCD = (x+3)(x+5)(x-3)

Now, get the numerator...

(x-3) (2x+3) - (x-7)(x+3) I get this from dividing the LCD to their denominator... (x+3)(x+5)(x-3) / (x+3)(x+5) = x-3... then I multiplied it to the numerator...

Now we have....

{ (x-3) (2x+3) - (x-7) (x+3) } / (x+3) (x+5) (x-3)

Then simplify...

(2x^2 -3x -9 - x^2 +4x +21) / (x+3) (x^2 +2x -15)

(x^2 +x +12) / x^3 +2x^2 -15 +3x^2 +6x -45

Final answer ---> (x^2 +x +12) / (x^3 +5x^2 +6x -60)

I'm not sure... But better study it in visiting other sites...

Answer 2

1. First factorize the denominator of both terms.

x^2 +8x+15= (x+3) (x+5)    and

x^2+2x-15= (x+5) (x-3)

2. The expression now becomes:

  2x+3/ (x+3) (x+5) (minus) x-7 / (x+5) (x-3)

3. Take LCM:



  [(2x+3) (x-3) - (x-7) (x+3)] / [(x+5)(x-3) (x+3)

=  x^2 +x +12 / (x+5) (x-3) (x+3)

= answer....

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