Question

What is the simplified form of 2 over x squared minus x minus 1 over x ?

x minus 1 over the quantity x times x plus 1

1 minus x over the quantity x times x plus 1

3 minus x over the quantity x times x minus 1

x plus 2 over the quantity x times x minus 1

Answer 1

\[\frac{ 2 }{ x^2 - x } - \frac{ 1 }{ x }\]

Right?

Answer 2

Well assuming it IS that....notice how the 1st denominator can be factored...

\[\frac{ 2 }{ x(x - 1) } - \frac{ 1 }{ x }\]

Notice now that all we have to do...is multiply the second fraction by (x - 1) to have a common denominator... So this would come out to ...

\[\frac{ 2 }{ x(x - 1) } - \frac{ 1 }{ x } \times \frac{(x - 1)}{(x - 1)}\]

Simplified down a bit and we have

\[\frac{ 2 }{ x(x - 1) } - \frac{ x - 1 }{ x(x - 1) }\]

We can now put these over the common denominator

\[\frac{ 2 - (x - 1) }{ x(x - 1) }\]

Lets simplify the top a bit...distribute the '-' sign...

\[\frac{ 2 - x + 1 }{ x(x - 1) }\]

And finally we arrive at...

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

Which answer choice is that?