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Heres the equation: x+6/x-3=2x/x-3.

 

What are the domain restrictions, if there are any, for the equation? 

What is the LCD?

Multiply the equation by the LCD and state the resulting equation in standard form.

Solve and state solutions in simplest form.

 

Thank you. Any help would do.

Guest Nov 27, 2017

Best Answer 

 #1
avatar+5587 
+3

Assuming that the equation is this...

 

(x + 6) / (x - 3)  =  2x / (x - 3)

 

Any  x  value that causes a zero in a denominator is excluded from the domain.

So, we can't have

 

x - 3  =  0

x  =  3         This is the only value that is restricted.

 

The two fractions already have a common denominator of  x - 3  ,  so the LCD is just  x - 3 .

 

(x + 6) / (x - 3)  =  2x / (x - 3)               Multiply both sides by  x - 3 .

 

x + 6  =  2x        Subtract  2x  from both sides, then multiply both sides by  -1 .

 

x - 6  =  0           I think this is the standard form.

 

To solve for  x , add  6  to both sides.

 

x  =  6                And  6  is not a restricted value.  x = 6  is the only solution.

hectictar  Nov 27, 2017
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1+0 Answers

 #1
avatar+5587 
+3
Best Answer

Assuming that the equation is this...

 

(x + 6) / (x - 3)  =  2x / (x - 3)

 

Any  x  value that causes a zero in a denominator is excluded from the domain.

So, we can't have

 

x - 3  =  0

x  =  3         This is the only value that is restricted.

 

The two fractions already have a common denominator of  x - 3  ,  so the LCD is just  x - 3 .

 

(x + 6) / (x - 3)  =  2x / (x - 3)               Multiply both sides by  x - 3 .

 

x + 6  =  2x        Subtract  2x  from both sides, then multiply both sides by  -1 .

 

x - 6  =  0           I think this is the standard form.

 

To solve for  x , add  6  to both sides.

 

x  =  6                And  6  is not a restricted value.  x = 6  is the only solution.

hectictar  Nov 27, 2017

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