Please help! Subtract:
x/x+2 - 1/x-2

Question

anonymous · Answer

Your common denominator will be the product of both denominators.  That is
$$(x-2)(x+2)$$
Your numerator of the first term will need to be multiplied by x-2 (because the top and bottom both need to be multiplied by x-2)
Your numerator of the second term will need to be multiplied by x+2.
$$(x(x-2))/((x+2)(x-2)) + (1(x+2))/((x+2)(x-2))$$
Since you have the same denominator, you can just add the numerators.
$$(x(x-2)+(x+2))/((x+2)(x-2))$$
Simplifying...$$(x^2-2x+x+2)/((x+2)(x-2))$$$$(x^2-x+2)/((x+2)(x-2))$$
Next, you need to factor the top.
$$((x-2)(x+1))/((x+2)(x-2))$$
The x-2 on top will cancel with the x-2 on bottom.
$$(x+1)/(x+2)$$
That should do it.  Let me know if you have any questions.