Algebra Examples

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

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

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

Step 2

Solve the equation for $x$ .

Tap for more steps...

Step 2.1

Rewrite the equation as ${(x - 2)}^{\frac{1}{2}} \cdot 1 = 1 \cdot 2$ .

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

Step 2.2

Move the terms containing $x$ to the left side and simplify.

Tap for more steps...

Step 2.2.1

Multiply ${(x - 2)}^{\frac{1}{2}}$ by $1$ .

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

Step 2.2.2

Multiply $2$ by $1$ .

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

Step 2.3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 2.4

Simplify the exponent.

Tap for more steps...

Step 2.4.1

Simplify the left side.

Tap for more steps...

Step 2.4.1.1

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

Tap for more steps...

Step 2.4.1.1.1

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

Tap for more steps...

Step 2.4.1.1.1.1

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

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

Step 2.4.1.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.1.1.1.2.1

Cancel the common factor.

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

Step 2.4.1.1.1.2.2

Rewrite the expression.

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

Step 2.4.1.1.2

Simplify.

$x - 2 = 2^{2}$

Step 2.4.2

Simplify the right side.

Tap for more steps...

Step 2.4.2.1

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

$x - 2 = 4$

Step 2.5

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

Tap for more steps...

Step 2.5.1

Add $2$ to both sides of the equation.

$x = 4 + 2$

Step 2.5.2

Add $4$ and $2$ .

$x = 6$