How do you solve the rational equation #1 / (x+1) = (x-1)/ x + 5/x#?

1 Answer
Jan 9, 2016

Answer:

#x=-2#

Explanation:

#1/(x+1)=(x-1)/x+5/x#

First, recognize that the fractions on the right hand side can be added since they have the same denominator.

#1/(x+1)=(x-1+5)/x#

#1/(x+1)=(x+4)/x#

Now, cross multiply.

#x*1=(x+4)*(x+1)#

You will have to FOIL on the right hand side.

#x=x^2+x+4x+4#

#0=x^2+4x+4#

From here, you could find the roots by using the quadratic formula, completing the square, or simply by factoring and recognizing this is a perfect square trinomial.

#0=(x+2)^2#

#0=x+2#

#x=-2#

When working with rational functions, always check that this won't cause any domain errors (making a denominator equal #0#). In this case, that won't happen.