Algebra Examples

$\frac{3 x - 4}{x - 5} = \frac{3 x + 6}{x + 2}$

Step 1

Factor each term.

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Step 1.1

Factor $3$ out of $3 x + 6$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 x - 4}{x - 5} = \frac{3 (x) + 6}{x + 2}$

Step 1.1.2

Factor $3$ out of $6$ .

$\frac{3 x - 4}{x - 5} = \frac{3 x + 3 \cdot 2}{x + 2}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 x - 4}{x - 5} = \frac{3 (x + 2)}{x + 2}$

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{3 (x + 2)}{x + 2}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 x - 4}{x - 5} = \frac{3 (x + 2)}{x + 2}$

Step 1.2.1.2

Rewrite the expression.

$\frac{3 x - 4}{x - 5} = \frac{3}{1}$

Step 1.2.2

Divide $3$ by $1$ .

$\frac{3 x - 4}{x - 5} = 3$

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.

$x - 5, 1$

Step 2.2

Remove parentheses.

$x - 5, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x - 5$

Step 3

Multiply each term in $\frac{3 x - 4}{x - 5} = 3$ by $x - 5$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{3 x - 4}{x - 5} = 3$ by $x - 5$ .

$\frac{3 x - 4}{x - 5} (x - 5) = 3 (x - 5)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x - 4}{x - 5} (x - 5) = 3 (x - 5)$

Step 3.2.1.2

Rewrite the expression.

$3 x - 4 = 3 (x - 5)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$3 x - 4 = 3 x + 3 \cdot - 5$

Step 3.3.2

Multiply $3$ by $- 5$ .

$3 x - 4 = 3 x - 15$

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 $3 x$ from both sides of the equation.

$3 x - 4 - 3 x = - 15$

Step 4.1.2

Combine the opposite terms in $3 x - 4 - 3 x$ .

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Step 4.1.2.1

Subtract $3 x$ from $3 x$ .

$0 - 4 = - 15$

Step 4.1.2.2

Subtract $4$ from $0$ .

$- 4 = - 15$

Step 4.2

Since $- 4 \neq - 15$ , there are no solutions.

No solution