Simplify the following by first finding the lowest common denominator.
2/(x+3) + 3/(x-5)

Question

Simplify the following by first finding the lowest common denominator. 
2/(x+3) + 3/(x-5)

e.mccormick · Answer

$$\frac{2}{x+3}+\frac{3}{x-5}$$LCD works the same in algebra as it does in fractions.  For example:
$$\frac{1}{2}+\frac{2}{3}=\frac{1\times 3}{2\times 3}+\frac{2\times 2}{3\times 2}$$

e.mccormick · Answer

If you do that same basic thing and multiply the (x-5) on the right to the top and bottom of the one on the left that will give it a denominator that can be added.  At the same time, you mutliply (x+3) on the left times both the top and bottom of the right.

Once you have that common denominatior, you can do the addition.  Then it becomes a simplification problem.

anonymous · Answer

that means it simplifies to 
$$\frac{ 5x-1 }{ (x+3)(x-5)}$$

e.mccormick · Answer

Yah, and there are no factors below that match the above so that is a good answer.  It is the fully factored form, which most teachers like.

anonymous · Answer

okay thankyou

e.mccormick · Answer

np.  have fun!