How do you solve 6/(x-1) = 9/(x+1)?

1 Answer
Oct 5, 2016

x=5

Explanation:

This is a rational equation therefore we have to lead it in a canonical form like:

(N(x))/(D(x))=0

In order to do this we have to move all the terms on LHS:

6/(x-1)=9/(x+1)=>6/(x-1)-9/(x+1)=0

Now we could find LCD (less common denominator) that is:

LCD=(x-1)(x+1)

Since a denominator cannot never be zero we have to find the x values that make it zero and exclude them from the solutions of the equation.

(x-1)(x+1)=0

This is a product, then it's zero when the factors are zero.

(x+1)=0=>x=-1
(x-1)=0=>x=1

:. x!=+-1

Now we can simplyfy the fractions:

(6(x+1)-9(x-1))/((x+1)(x-1))=0

and we can simplify the LCD

(6(x+1)-9(x-1))/color(green)cancel((x+1)(x-1))=0

Move all the x therms on the LHS and the other one on RHS

6x-9x=-6-9

-3x=-15

cancel(-)3x=cancel(-)15

3x=15

x=cancel(15)^5/cancel(3)=5

x=5

graph{6/(x-1)-9/(x+1) [4.438, 6.335, -0.688, 0.26]}