2x/x+4=x/x-1

Question

2x/x+4=x/x-1

Answer 1

Hi Erin,

 

2x/x+4=x/x-1

 

cross multiply both the sides 

 

2x(x-1)=x(x+4)

 

2x²-2x=x²+4x

 

2x²-x²-2x-4x=0

 

x²-6x=0

 

x(x-6)=0

 

x=0  or  (x-6)=0

 

x=0 or x=6

Answer 2

The easiest way to solve this is by cross multiplying: 2x(x-1) and (x+4)x

 

That yields 2x² - 2x = x²  + 4x

 

Then you move everything over to the left side of the equation, by subtracting both terms (since they are positive) so that you are left with zero on the right hand side.

 

Now you have:  x² - 6x= 0

 

This can now be factored using the greatest common factor of x and getting: x(x - 6) = 0. If the product of two terms is 0, one of the terms must be equal to zero, so either: x = 0 or x-6 = 0. So the tentative solutions are x = 0 and x =6. Then we check our answers and see that both work.