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I am working on advanced functions homework (pre calc) and I am stuck on a question involving rational equations. I was wondering if someone could help with the answer.

1/x - 4 = 1/x+2

If you could show the solution that would be great.

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I don't have enough time to show you everything, but you should check out this: https://www.khanacademy.org/ It really helped me through university when things got rough

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Is the answer "no solution"? I haven't done this in awhile. Don't judge. ##### Share on other sites

There is an app that you can take photos of questions and it will return answers.

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is that 1/(x + 2) or (1/x) + 2?

It was definitely not written down properly.

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Is the answer "no solution"? I haven't done this in awhile. Don't judge. If only it was that simple every time...

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Looks like you need a common denominator then quadratic formula. (try x(x+2))

If this is how you were asking easiest thing to do is check on wolfram alpha

http://www.wolframalpha.com/input/?i=(1%2Fx)-4%3D1%2F(x%2B2)

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1/(x+2)

Well that changes everything.

Nevermind. Wolfram Alpha says I'm wrong. LOL

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1/x - 4 = 1/(x+2)

1/x - 1/(x+2) = 4

(x+2-x)/[x(x+2)] = 4

2 = 4x2 + 8x

4x2 + 8x - 2 = 0

2(2x2 + 4x -1) = 0

Stick 2x2 + 4x - 1 = 0 into Quadratic equation

I THINK that's right. It matches Wolfram Alpha.

EDIT: I think I screwed up a sign, but it's sort of right.

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1/x - 4 = 1/(x+2)

1/x - 1/(x+2) = 4

(x+2-x)/[x(x+2)] = 4

2 = 4x2 + 8x

4x2 + 8x - 2 = 0

2(2x2 + 4x -1) = 0

Stick 2x2 + 4x - 1 = 0 into Quadratic equation

I THINK that's right. It matches Wolfram Alpha.

EDIT: I think I screwed up a sign, but it's sort of right.

You are correct.

OP whenever you have a problem of this nature, try to get all the unknowns out of the denominator.

1/x - 4 = 1/(x+2)

(1/x-4)(x+2) = 1

USE FOIL on the left hand side of the equation

1+2/x-4x-8 = 1

2/x-4x-8=0

There is only one term with x in the denominator so multiply by x and you will get the quadratic equation which goaltender interference posted.

Use the quadratic equation formula to solve given by:

x=[-b(+ or -) root(b^2-4ac)]/2a

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You are correct.

This makes me feel so much better. Good luck, OP.