Solve (a2)/(a-3) ⋅ (a2-2a-3)/(a2-6a)

Question

Simplify the expression

\frac{3}{2 a - 6}

Evaluate

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

Use the commutative property to reorder the terms

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

Use the commutative property to reorder the terms

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

Use the commutative property to reorder the terms

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

Subtract the terms

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Evaluate

2 a - 2 a - 3

The sum of two opposites equals 0

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Evaluate

2 a - 2 a

Collect like terms

(2 - 2) a

Add the coefficients

0 \times a

Calculate

0

0 - 3

Remove 0

- 3

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

Subtract the terms

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Simplify

2 a - 6 a

Collect like terms by calculating the sum or difference of their coefficients

(2 - 6) a

Subtract the numbers

- 4 a

\frac{2 a}{a - 3} \times \frac{- 3}{- 4 a}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{2 a}{a - 3} \times \frac{3}{4 a}

Cancel out the common factor 2

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

Cancel out the common factor a

\frac{1}{a - 3} \times \frac{3}{2}

Multiply the terms

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

Multiply the terms

\frac{3}{2 ( a - 3 )}

Solution

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Evaluate

2 (a - 3)

Apply the distributive property

2 a - 2 \times 3

Multiply the numbers

2 a - 6

\frac{3}{2 a - 6}

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Find the excluded values

a = 3, a = 0

Evaluate

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

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

a - 3 = 0 a \times 2 - 6 a = 0

Solve the equations

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Evaluate

a - 3 = 0

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

a = 0 + 3

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

a = 3

a = 3 a \times 2 - 6 a = 0

Solve the equations

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Evaluate

a \times 2 - 6 a = 0

Simplify

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Evaluate

a \times 2 - 6 a

Use the commutative property to reorder the terms

2 a - 6 a

Collect like terms by calculating the sum or difference of their coefficients

(2 - 6) a

Subtract the numbers

- 4 a

- 4 a = 0

Change the signs on both sides of the equation

4 a = 0

Rewrite the expression

a = 0

a = 3 a = 0

Solution

a = 3, a = 0

Show Solution

Find the roots

a \in \emptyset

Evaluate

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

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

\frac{a \times 2}{a - 3} \times \frac{a \times 2 - 2 a - 3}{a \times 2 - 6 a} = 0

Find the domain

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Evaluate

{a - 3 \neq = 0 a \times 2 - 6 a \neq = 0

Calculate

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Evaluate

a - 3 \neq = 0

Move the constant to the right side

a \neq = 0 + 3

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

a \neq = 3

{a \neq = 3 a \times 2 - 6 a \neq = 0

Calculate

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Evaluate

a \times 2 - 6 a \neq = 0

Simplify

- 4 a \neq = 0

Change the signs on both sides of the equation

4 a \neq = 0

Rewrite the expression

a \neq = 0

{a \neq = 3 a \neq = 0

Find the intersection

a \in (- \infty, 0) \cup (0, 3) \cup (3, + \infty)

\frac{a \times 2}{a - 3} \times \frac{a \times 2 - 2 a - 3}{a \times 2 - 6 a} = 0, a \in (- \infty, 0) \cup (0, 3) \cup (3, + \infty)

Calculate

\frac{a \times 2}{a - 3} \times \frac{a \times 2 - 2 a - 3}{a \times 2 - 6 a} = 0

Use the commutative property to reorder the terms

\frac{a \times 2}{a - 3} \times \frac{2 a - 2 a - 3}{a \times 2 - 6 a} = 0

Subtract the terms

\frac{a \times 2}{a - 3} \times \frac{0 - 3}{a \times 2 - 6 a} = 0

Use the commutative property to reorder the terms

\frac{a \times 2}{a - 3} \times \frac{0 - 3}{2 a - 6 a} = 0

Use the commutative property to reorder the terms

\frac{2 a}{a - 3} \times \frac{0 - 3}{2 a - 6 a} = 0

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

\frac{2 a}{a - 3} \times \frac{- 3}{2 a - 6 a} = 0

Subtract the terms

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Simplify

2 a - 6 a

Collect like terms by calculating the sum or difference of their coefficients

(2 - 6) a

Subtract the numbers

- 4 a

\frac{2 a}{a - 3} \times \frac{- 3}{- 4 a} = 0

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{2 a}{a - 3} \times \frac{3}{4 a} = 0

Multiply the terms

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Multiply the terms

\frac{2 a}{a - 3} \times \frac{3}{4 a}

Cancel out the common factor 2

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

Cancel out the common factor a

\frac{1}{a - 3} \times \frac{3}{2}

Multiply the terms

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

Multiply the terms

\frac{3}{2 ( a - 3 )}

\frac{3}{2 ( a - 3 )} = 0

Cross multiply

3 = 2 (a - 3) \times 0

Simplify the equation

3 = 0

Solution

a \in \emptyset

Show Solution