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a simple (annoying) equasion - HSN forum

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a simple (annoying) equasion

Started by Sep, Sep 10 2009 09:50 PM

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#1 Sep

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Posted 10 September 2009 - 09:50 PM

(6/x) - (6/x+1) = 1

solve for x

this was part of a larger question, which i have taken to this stage

i know x = 2
but... i cant get the steps to finish it off

its such a silly thing but i cant put my finger on the working

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#2 Amanda H

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Posted 10 September 2009 - 11:17 PM

Treat this question as you would if it was a normal fraction question with only numbers and no 'x'

Start by creating a common denominator so you can carry out the subtraction:

$\frac{6(x+1)}{x(x+1)} - \frac{6x}{x(x+1)} = \frac{x(x+1)}{x(x+1)}$

Expand the brackets

$\frac{6x+6-6x}{x(x+1)}=\frac{x(x+1)}{x(x+1)}$

Collect terms on the left

$\frac{6}{x(x+1)}=\frac{x(x+1)}{x(x+1)}$

Multiply through by the denominator

6 = x(x+1)

6 = x(x+1)

Expand right hand side

6 = x^2+x

6 = x^2+x

Move everything to one side leaving 0 on the other

x^2+x-6=0

x^2+x-6=0

Factorise

(x-2)(x+3) = 0

If the only answer is x=2 then I'm assuming the answer is a measurement or something and not allowed to be negative.

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#3 Sep

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Posted 11 September 2009 - 05:58 AM

many thanks Amanda H,
i still cant believe i had problems solving this

need to practice some me thinks

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