Question

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

Answer 1

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.