Solve 1/(2x+1) > x/(3x-2)

I've so far done 1/(2x+1) - x/(3x-2) > 0

(2x^2 + 2x -2)/(2x+1)(3x-2) > 0

Now I know that I have to make the top line zero, but it doesn't factorise. Any help?

Thanks.

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- June 15th 2009, 12:00 PMErghhhInequalities
Solve 1/(2x+1) > x/(3x-2)

I've so far done 1/(2x+1) - x/(3x-2) > 0

(2x^2 + 2x -2)/(2x+1)(3x-2) > 0

Now I know that I have to make the top line zero, but it doesn't factorise. Any help?

Thanks. - June 15th 2009, 12:07 PMstapel
Hint:

**Quadratic Formula**. (Wink) - June 15th 2009, 12:09 PMcraig
You wouldn't be studying for an FP2 exam would you by any chance ;) ?

Try multiplying both sides by

This gives you

A little rearranging gives you

Giving you critical values of and , if you look at the discriminant of the other equation you will notice that it is less than zero, there no real roots.

Using your graphic calculator if you have one, draw the graph of , and look to see when it satisfies the inequality.

Hope this helps - June 15th 2009, 12:24 PMErghhh
Ahh thank you! I will be doing fp2 on friday, but I found this baby in an fp1 past paper!

- June 15th 2009, 12:26 PMcraig