Answer
$x = 1$
Work Step by Step
Rewrite the problem in radical form. Remember that $a^{\frac{m}{n}}$ can be rewritten in radical form as $\sqrt[n] {a^{m}}$:
$\sqrt {7x + 6} - \sqrt {9 + 4x} = 0$
Add $\sqrt {9 + 4x}$ to both sides of the equation:
$\sqrt {7x + 6} = \sqrt {9 + 4x}$
Since the indices are the same for both radicals, we can square both sides of the equation to eliminate the radicals:
$7x + 6 = 9 + 4x$
Subtract $4x$ from each side of the equation to move the variables to the left side of the equation:
$3x + 6 = 9$
Subtract $6$ from each side of the equation to move the constants to the right side of the equation:
$3x = 3$
Divide each side of the equation by $3$:
$x = 1$
To check if we have an extraneous solution, we substitute the solution into the original equation to see if the two sides equal one another:
$\sqrt {7(1) + 6} - \sqrt {9 + 4(1)} = 0$
Simplify the radicands:
$\sqrt {13} - \sqrt {13}=0\\
0=0$
Both sides are equal; therefore, this solution is valid.
