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**[SOLVED] Alegrabic Fraction Simplification**

## 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 :)