Algebra Examples

$\frac{x - 7}{2 x - 6} \sqrt{x - 3} = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$\frac{x - 7}{2 x - 6} = 0$

$\sqrt{x - 3} = 0$

Step 2

Set $\frac{x - 7}{2 x - 6}$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $\frac{x - 7}{2 x - 6}$ equal to $0$ .

$\frac{x - 7}{2 x - 6} = 0$

Step 2.2

Solve $\frac{x - 7}{2 x - 6} = 0$ for $x$ .

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Step 2.2.1

Set the numerator equal to zero.

$x - 7 = 0$

Step 2.2.2

Add $7$ to both sides of the equation.

$x = 7$

Step 3

Set $\sqrt{x - 3}$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $\sqrt{x - 3}$ equal to $0$ .

$\sqrt{x - 3} = 0$

Step 3.2

Solve $\sqrt{x - 3} = 0$ for $x$ .

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Step 3.2.1

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

${\sqrt{x - 3}}^{2} = 0^{2}$

Step 3.2.2

Simplify each side of the equation.

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Step 3.2.2.1

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

${({(x - 3)}^{\frac{1}{2}})}^{2} = 0^{2}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

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

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Step 3.2.2.2.1.1

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

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Step 3.2.2.2.1.1.1

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

${(x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.2.2.1.1.2.1

Cancel the common factor.

${(x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.2.2.1.1.2.2

Rewrite the expression.

${(x - 3)}^{1} = 0^{2}$

Step 3.2.2.2.1.2

Simplify.

$x - 3 = 0^{2}$

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Raising $0$ to any positive power yields $0$ .

$x - 3 = 0$

Step 3.2.3

Add $3$ to both sides of the equation.

$x = 3$

Step 4

The final solution is all the values that make $\frac{x - 7}{2 x - 6} \cdot \sqrt{x - 3} = 0$ true.

$x = 7, 3$

Step 5

Exclude the solutions that do not make $\frac{x - 7}{2 x - 6} \cdot \sqrt{x - 3} = 0$ true.

$x = 7$