Maths Problem

[grasscarp]

I can't find a special section for Maths questions in Topics, so will post it here in the hope that someone can help. It is for a child whose teacher would not explain it to him (or give the answer!)

2x over x-1 minus 7x -3 over x squared - 1

The answer and bit of guidance with how to tackle the problem would be much appreciated.

[squarebear]

Can I ask how old this child is?

[bibblebub]

last line should be (if done properly):

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

[willyjmartin]

2x/(x-1) - (7x-3)/(xsquared-1) = [2x(x+1)-(7x-3)]/(x-1)(x+1)]
=2x squared +2x -7x +3)/(x-1)(x+1)
=(x-1)(2x-3)/(x-1)(x+1)
=(2x-3)/(x+1)

note xsquared-1 = (x-1)(x+1)

[willyjmartin]

Please ignore all other workings than DR B and myself as the answer is
(2x-3)/(x+1) i.e reduced to its lowest form

[grasscarp]

A huge thank you to input from piggynose, quinie, mickrog, bibblebub, willyjmartin, old geezer, jsnhghs, dr b and ellipsis. The child is around 13 years old Squarebear. I will get him to ask the teacher what is the answer when I see him tomorrow, and if/when the teacher does what teachers are supposed to do, I will let you all know what he says.

[Ellipsis]

I agree willyjmartin. More haste, less correctness on my part, I'm afraid.

There are a couple of bracket errors in your solution however.

To talk grasscarp through it ...

2x/(x-1) - (7x-3)/(x^2 - 1)

Factorise the (x^2-1) ... gives (x+1)(x-1)

2x/(x-1) - (7x-3)/((x+1)(x-1))

Provide a common denominator by mutiply the top and bottom of the first expression by (x+1)

2x(x+1)/((x+1)(x-1)) - (7x-3)/((x+1)(x-1))

Multiply out the numerator (top) of the first expression and put the whole lot over the common denominator:

(2x^2 +2x -7x +3)/((x+1)(x-1))

Simplify:

(2x^2 -5x +3)/((x+1)(x-1))

Factorise 2x^2 - 5x +3 ... gives (2x -3)(x-1)

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

Cancel (x-1) from top and bottom:

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

[grasscarp]

Special accolade to Dr B for being the first to get it right, second to Willyjmartin for also getting it, and to Ellipsis for going through it line by line. I have now got my head round it!