MYTUTOR SUBJECT ANSWERS

207 views

Find the set of values for which: 3/(x+3) >(x-4)/x

First we must consider for which values of x the equation: 3/(x+3) = (x-4)/x is undefined. In this case, x=-3, and x=0. 

Now we must consider each of the cases, x<-3, -3

Case 1 (x<-3): if we assume 3/(x+3) > (x-4)/x then it follows, as x<-3, 3x > x2-x-12. Which implies (x-6)(x+2) < 0. For this to hold exactly one of (x-6) and (x+2) must be less than 0 and the other greater than 0. which implies -2

Case 2 (-32-4x-12 > 0, which implies (x-6)(x+2) >0. Therefore for x2-4x-12 > 0, either both (x-6) and (x+2) must be less than 0 or greater than 0. therefore x<-2 or x>6. Therefore as we know -3

Case 3 (x>0): Therefore x2-4x-12 < 0, which implies (x-6)(x+2) < 0. For this to hold exactly one of (x-6) and (x+2) must be less than 0 and the other greater than 0. which implies -2

Finally as we have considered all cases the final answer is -3

David M. A Level Maths tutor, GCSE Maths tutor, A Level Further Mathe...

6 months ago

Answered by David, an A Level Further Mathematics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

90 SUBJECT SPECIALISTS

£20 /hr

Nigel M.

Degree: Economics and maths (Bachelors) - Bath University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
-Personal Statements-

“First year Economics and Maths student here to help you out with A-level or GCSE maths and physics!”

MyTutor guarantee

£20 /hr

Sara D.

Degree: Computer Science and Mathematics (Bachelors) - Edinburgh University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
Computing

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£20 /hr

Laurie D.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Further Mathematics , Maths

Further Mathematics
Maths

“1st year Maths student at Warwick, after a few tutorials you'll see Maths isn't the scary, hard subject most people think it is - it's actually really fun! ”

MyTutor guarantee

About the author

David M.

Currently unavailable: for new students

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Maths

Further Mathematics
Maths

“Me: I am a second year maths student at Warwick University. I have always loved maths and very much enjoy finding solutions for problems and also alternative ways to approach them.  I am a calm individual who has helped a number of s...”

MyTutor guarantee

You may also like...

Other A Level Further Mathematics questions

Prove by induction that 11^n - 6 is divisible by 5 for all positive integer n.

How to use the integrating factor?

What is a complex number?

How do you show that the centre of a group is a subgroup

View A Level Further Mathematics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok