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Further Maths question help

Hi guys, I am stuck on this question.

Solve the following inequality: [x/x-1] ≤ 2x x≠1

This is on exercise 1A question 5 in the further maths edexcel FP2 book.

The book suggest to square the (x-1) and multiply both sides and after this and then rearrange the formula, I am stuck on the rearrangement part.

I dont get how to do this, and have tried I'm stuck on what to do after multiplying by the (x-1)
Please Help

Reply 1

ermm

after you've multiplied by (x-1)^2 on both sides, you're left with x(x-1) ≤ 2x (x-1)^2
You can then expand both sides and rearrange so on one side of the inequality, you get a cubic function and on the other side, a number.

So after expanding:

x^2 - x ≤ 2x^3 - 4x^2 + 2x

Then simplify so:

2x^3 -5x^2 + 3x >= 0

x(2x^2 - 5x + 3) >= 0

x(2x - 3)(x - 1) >=0

so you know the three critical values and you can draw the graph

Reply 2

fnatic NateDestiel

Original post by ermm

you are a hero. Ive been stuck on these kind of questions for so long.
So the best thing to do is to expand and then simplify, also is 0 always a critical value, thanks x