Solve 2/((2/(x-3)) 3)

Question

Simplify the expression

\frac{x - 3}{3}

Evaluate

\frac{2}{( \frac{2}{x - 3} ) \times 3}

Remove the unnecessary parentheses

\frac{2}{\frac{2}{x - 3} \times 3}

Multiply the terms

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Multiply the terms

\frac{2}{x - 3} \times 3

Multiply the terms

\frac{2 \times 3}{x - 3}

Multiply the terms

\frac{6}{x - 3}

\frac{2}{\frac{6}{x - 3}}

Multiply by the reciprocal

2 \times \frac{x - 3}{6}

Cancel out the common factor 2

1 \times \frac{x - 3}{3}

Solution

\frac{x - 3}{3}

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Find the excluded values

x = 3

Evaluate

\frac{2}{( \frac{2}{x - 3} ) \times 3}

To find the excluded values,set the denominators equal to 0

x - 3 = 0 (\frac{2}{x - 3}) \times 3 = 0

Solve the equations

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Evaluate

x - 3 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

x = 3

x = 3 (\frac{2}{x - 3}) \times 3 = 0

Solve the equations

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Evaluate

(\frac{2}{x - 3}) \times 3 = 0

Simplify

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Evaluate

(\frac{2}{x - 3}) \times 3

Remove the unnecessary parentheses

\frac{2}{x - 3} \times 3

Multiply the terms

\frac{2 \times 3}{x - 3}

Multiply the terms

\frac{6}{x - 3}

\frac{6}{x - 3} = 0

Cross multiply

6 = (x - 3) \times 0

Simplify the equation

6 = 0

The statement is false for any value of x

x \in \emptyset

x = 3 x \in \emptyset

Solution

x = 3

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Find the roots

x \in \emptyset

Evaluate

\frac{2}{( \frac{2}{x - 3} ) \times 3}

To find the roots of the expression,set the expression equal to 0

\frac{2}{( \frac{2}{x - 3} ) \times 3} = 0

Find the domain

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Evaluate

{x - 3 \neq = 0 (\frac{2}{x - 3}) \times 3 \neq = 0

Calculate

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Evaluate

x - 3 \neq = 0

Move the constant to the right side

x \neq = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

x \neq = 3

{x \neq = 3 (\frac{2}{x - 3}) \times 3 \neq = 0

Calculate

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Evaluate

(\frac{2}{x - 3}) \times 3 \neq = 0

Simplify

\frac{6}{x - 3} \neq = 0

Multiply both sides

\frac{6}{x - 3} \times (x - 3) \neq = 0 \times (x - 3)

Evaluate

6 \neq = 0 \times (x - 3)

Multiply both sides

6 \neq = 0

The statement is true for any value of x

x \in R

{x \neq = 3 x \in R

Find the intersection

x \neq = 3

\frac{2}{( \frac{2}{x - 3} ) \times 3} = 0, x \neq = 3

Calculate

\frac{2}{( \frac{2}{x - 3} ) \times 3} = 0

Remove the unnecessary parentheses

\frac{2}{\frac{2}{x - 3} \times 3} = 0

Multiply the terms

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Multiply the terms

\frac{2}{x - 3} \times 3

Multiply the terms

\frac{2 \times 3}{x - 3}

Multiply the terms

\frac{6}{x - 3}

\frac{2}{\frac{6}{x - 3}} = 0

Divide the terms

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Evaluate

\frac{2}{\frac{6}{x - 3}}

Multiply by the reciprocal

2 \times \frac{x - 3}{6}

Cancel out the common factor 2

1 \times \frac{x - 3}{3}

Multiply the terms

\frac{x - 3}{3}

\frac{x - 3}{3} = 0

Simplify

x - 3 = 0

Move the constant to the right side

x = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

x = 3

Check if the solution is in the defined range

x = 3, x \neq = 3

Solution

x \in \emptyset

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