(5x)/(x-8)=(4x+8)/(x-8)

Question

Image of equation:

 

Options: 

 

 

x =8

x = −2

 

x = −2 or x = 8

 

no solution

Answer 1

Option 1 fails because if x = 8, then the denominator will be +8 - 8 which is zero.

 

Option 2 fails because when we substitute -2 for x, we get 5(-2)/-2-8 = [4(-2) + 8]/-2-8, which becomes -10/-10 = (-8+8)/-10, which becomes -1 = 0/-10, which becomes -1 = 0, which is false.

 

Option 3 fails because of the results of #1 and #2.

 

The only option which can be selected is option 4, BUT, that option does not actually apply, because the equation is FALSE.

 

In fact, when any value for x is selected, the equation will produce a false result.

Answer 2

cross multiply to get x^2-16x+64=0

(x-8)(x-8)=0 implies x=8 but x can't be 8 because that would make the denominator 0

another way to solve...

x can't be 8 and -2 makes the left side equal to 1 and makes the right side equal to 0

the answer is "no solution"