Question

7 fill in the blank 1 point
what is the solution of the following equation? $\frac{14}{x+2}-6=\frac{2}{x+2}$
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Explanation:

Step1: Eliminate denominator

Multiply all terms by $x+2$ (where $x
eq -2$):
$14 - 6(x+2) = 2$

Step2: Expand the bracket

Calculate $6(x+2)$:
$14 - 6x - 12 = 2$

Step3: Simplify left side

Combine constant terms:
$2 - 6x = 2$

Step4: Isolate variable term

Subtract 2 from both sides:
$-6x = 0$

Step5: Solve for x

Divide by -6:
$x = \frac{0}{-6} = 0$

Step6: Verify solution

Substitute $x=0$ back into original equation:
$\frac{14}{0+2} - 6 = 7 - 6 = 1$, and $\frac{2}{0+2} = 1$. Both sides are equal, so solution is valid.

Answer:

$0$