Algebra Examples

$\frac{(x + 4) (x - 2)}{9 (x - 2)} = \frac{x + 4}{9}$

Step 1

Reduce the expression $\frac{(x + 4) (x - 2)}{9 (x - 2)}$ by cancelling the common factors.

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Step 1.1

Cancel the common factor.

$\frac{(x + 4) (x - 2)}{9 (x - 2)} = \frac{x + 4}{9}$

Step 1.2

Rewrite the expression.

$\frac{x + 4}{9} = \frac{x + 4}{9}$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$9, 9$

Step 2.2

Since $9, 9$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $9, 9$ then find LCM for the variable part .

Step 2.3

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 2.4

$9$ has factors of $3$ and $3$ .

$3 \cdot 3$

Step 2.5

Multiply $3$ by $3$ .

$9$

Step 3

Multiply each term in $\frac{x + 4}{9} = \frac{x + 4}{9}$ by $9$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{x + 4}{9} = \frac{x + 4}{9}$ by $9$ .

$\frac{x + 4}{9} \cdot 9 = \frac{x + 4}{9} \cdot 9$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $9$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x + 4}{9} \cdot 9 = \frac{x + 4}{9} \cdot 9$

Step 3.2.1.2

Rewrite the expression.

$x + 4 = \frac{x + 4}{9} \cdot 9$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $9$ .

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Step 3.3.1.1

Cancel the common factor.

$x + 4 = \frac{x + 4}{9} \cdot 9$

Step 3.3.1.2

Rewrite the expression.

$x + 4 = x + 4$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $x$ from both sides of the equation.

$x + 4 - x = 4$

Step 4.1.2

Combine the opposite terms in $x + 4 - x$ .

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Step 4.1.2.1

Subtract $x$ from $x$ .

$0 + 4 = 4$

Step 4.1.2.2

Add $0$ and $4$ .

$4 = 4$

Step 4.2

Since $4 = 4$ , the equation will always be true.

Always true

Step 5

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$