# #7/(z+1) - z - 5/(z^2-1) = 6/z# ? P.S. I have no idea on how to solve this problem.

##### 2 Answers

Given:

We need to find a common denominator

Observe that

So I choose the common denominator to be

We need to 'force' each fraction to have this as its denominator.

So we start with:

Now we start to change things. I am not changing the RHS side as I can 'get rid' of the z denominator by cross multiplying.

The equation gets folded over 2 lines due to its length

Multiply both sides by

Multiply both sides by

Hence

I do not know how to take it on from this point!

I will ask another contributor I know to take a look!

#### Explanation:

I think the equation in the question should be:

#7/(z+1)-(z-5)/(z^2-1)=6/z#

Note that

So in order to change this rational equation into a polynomial one, we can multiply by

#7z(z-1)-z(z-5) = 6(z^2-1)#

which multiplies out to give:

#color(red)(cancel(color(black)(7z^2)))-7z-color(red)(cancel(color(black)(z^2)))+5z = color(red)(cancel(color(black)(6z^2)))-6#

The terms in

#-2z = -6#

Divide both sides by

#z = 3#

Finally we need to check that this is a valid solution by making sure that none of the denominators in the original equation are