Question

Simplify and leave your answer in factored form.
I'm going to post it after this! (:

Answer 1

\[ \frac{ \frac{ (x-5) }{ (x+5) } + \frac{ (x-1) }{ (x+1) } }{ \frac{ x }{ (x+1) }-\frac{ (3x-7) }{ x } }\]

Answer 2

In the end I got (2x(x^2 - 5)) / ((x +5)(2x^2-4x-7))

Answer 3

Multiply EVERY term by the inner LCD x(x+1)(x+5)

So

x(x+1)(x+5)[ (x-5)/(x+5)] = x(x+1)(x-5)

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x(x+1)(x+5)[ (x-1)/(x+1) ] = x(x+5)(x-1)

--------------

x(x+1)(x+5)[ x/(x+1) ] = x^2(x+5)

--------------

x(x+1)(x+5)[ (3x-7)/x ] = (x+1)(x+5)(3x-7)


===========================================

This means that

\[ \frac{ \frac{ (x-5) }{ (x+5) } + \frac{ (x-1) }{ (x+1) } }{ \frac{ x }{ (x+1) }-\frac{ (3x-7) }{ x } }\]

turns into

\[ \frac{ x(x+1)(x-5) + x(x+5)(x-1) }{ x^2(x+5)-(x+1)(x+5)(3x-7) }\]


I'll let you finish this

Answer 4

Oh, thanks!

Answer 5

Let me know what you get for the final answer