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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.

The square root of the quantity 2 x minus 7 end quantity equals 1.

Respuesta :

Answer:

Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .

1x − 2+1x + 2=4(x − 2)(x + 2)

(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)

(x−2)+(x+2)=4

2x=4

x=2

But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed!  .  Therefore, it cannot be a root of the original equation.  So, 2 is an extraneous solution. So, the equation has no solutions.

Step-by-step explanation: