Question

2/x + 2/x+1 - 2/x+2 can you show me your work to simplify this? and the restrictions?

Answer 1

You want to make the denominator the same for all 3 parts of it. So the bottom denominator would be \[x \left( x+1 \right)\left( x+2 \right)\]

Answer 2

So what you will get is:\[2(x+1)(x+2)/x(x+1)(x+2) + 2x(x+2)/x(x+1)(x+2) - 2x(x+1)/x(x+1)(x+2)\]

Answer 3

Now that the denominator is all the same, we can just focus on simplifying the numerator first. So, you will get: \[2(x+1)(x+2) +2x(x+2) - 2x(x+1) = 2(x ^{2}+3x+2) + 2x ^{2} +4x - 2x ^{2} -2x\]

Answer 4

Simplifying further:\[2x ^{2}+6x+4+2x ^{2}+4x-2x ^{2}-2x=2x ^{2}+8x+4=2(x ^{2}+4x+2)=2(x+2)^{2}\]

Answer 5

So your final equation is \[2(x+2)^{2}/x(x+1)(x+2) = 2(x+2)/x(x+1)\]

Answer 6

What are the restrictions?

Answer 7

Is that the final answer?

Answer 8

Sorry I did not reply you sooner. A restriction would be that your \[x(x+1)\neq0\]