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thomas49th
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[SOLVED] Alegrabic Fraction Simplification
Show that:
[tex]\frac{3x}{x+1} - \frac{x+7}{x^{2}-1}, x > 1[/tex]
can be written as:
[tex] 3 - \frac{4}{x-1}[/tex]
Well i can see the difference of 2 squares on the bottom of the second fraction
[tex]\frac{3x}{x+1} - \frac{x+7}{(x+1)(x-1)}[/tex]
cross multiply and x+1 cancels out
giving
[tex]\frac{3x(x-1)-(x+7)}{(x+1)(x-1)}[/tex]
the top factorises to (3x-7)(x+1) cancelling the (x+1)
giving me
[tex] \frac{3x-7}{x-1}[/tex]
But that doesn't equate to [tex] 3 - \frac{4}{x-1}[/tex] does it?
Where have i gone wrong
Thanks :)
Homework Statement
Show that:
[tex]\frac{3x}{x+1} - \frac{x+7}{x^{2}-1}, x > 1[/tex]
can be written as:
[tex] 3 - \frac{4}{x-1}[/tex]
The Attempt at a Solution
Well i can see the difference of 2 squares on the bottom of the second fraction
[tex]\frac{3x}{x+1} - \frac{x+7}{(x+1)(x-1)}[/tex]
cross multiply and x+1 cancels out
giving
[tex]\frac{3x(x-1)-(x+7)}{(x+1)(x-1)}[/tex]
the top factorises to (3x-7)(x+1) cancelling the (x+1)
giving me
[tex] \frac{3x-7}{x-1}[/tex]
But that doesn't equate to [tex] 3 - \frac{4}{x-1}[/tex] does it?
Where have i gone wrong
Thanks :)