Solve the Rational Equation for x square root of 3x-5-3 square root of x=0

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

Step 1

Add $3 \sqrt{x}$ to both sides of the equation.

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

Step 2

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

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

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 5}$ as ${(3 x - 5)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(3 x - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 5)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(3 \sqrt{x})}^{2}$ .

Simplify the expression.

Apply the product rule to $3 \sqrt{x}$ .

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

Raise $3$ to the power of $2$ .

$3 x - 5 = 9 {\sqrt{x}}^{2}$

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

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

$3 x - 5 = 9 {(x^{\frac{1}{2}})}^{2}$

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

$3 x - 5 = 9 x^{\frac{1}{2} \cdot 2}$

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

$3 x - 5 = 9 x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x - 5 = 9 x^{\frac{2}{2}}$

Rewrite the expression.

$3 x - 5 = 9 x^{1}$

Simplify.

$3 x - 5 = 9 x$

Step 4

Solve for $x$ .

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

Subtract $9 x$ from both sides of the equation.

$3 x - 5 - 9 x = 0$

Subtract $9 x$ from $3 x$ .

$- 6 x - 5 = 0$

Add $5$ to both sides of the equation.

$- 6 x = 5$

Divide each term in $- 6 x = 5$ by $- 6$ and simplify.

Divide each term in $- 6 x = 5$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{5}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{5}{- 6}$

Divide $x$ by $1$ .

$x = \frac{5}{- 6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{6}$

Step 5

Exclude the solutions that do not make $\sqrt{3 x - 5} - 3 \sqrt{x} = 0$ true.

$No solution$

Solve the Rational Equation for x square root of 3x-5-3 square root of x=0

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