Solve for x square root of 3x-1- square root of x+5=0

$\sqrt{3 x - 1} - \sqrt{x + 5} = 0$

Add $\sqrt{x + 5}$ to both sides of the equation.

$\sqrt{3 x - 1} = \sqrt{x + 5}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{3 x - 1}}^{2} = {\sqrt{x + 5}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 1}$ as ${(3 x - 1)}^{\frac{1}{2}}$ .

${({(3 x - 1)}^{\frac{1}{2}})}^{2} = {\sqrt{x + 5}}^{2}$

Simplify the left side.

Simplify ${({(3 x - 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 1)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(3 x - 1)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 5}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 1)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 5}}^{2}$

Rewrite the expression.

${(3 x - 1)}^{1} = {\sqrt{x + 5}}^{2}$

Simplify.

$3 x - 1 = {\sqrt{x + 5}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{x + 5}}^{2}$ as $x + 5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 5}$ as ${(x + 5)}^{\frac{1}{2}}$ .

$3 x - 1 = {({(x + 5)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 x - 1 = {(x + 5)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$3 x - 1 = {(x + 5)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x - 1 = {(x + 5)}^{\frac{2}{2}}$

Rewrite the expression.

$3 x - 1 = {(x + 5)}^{1}$

Simplify.

$3 x - 1 = x + 5$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$3 x - 1 - x = 5$

Subtract $x$ from $3 x$ .

$2 x - 1 = 5$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$2 x = 5 + 1$

Add $5$ and $1$ .

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

Solve for x square root of 3x-1- square root of x+5=0

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