Finite Math Examples

$\frac{v - 6}{v - 6} = \frac{v - 4}{v - 1} - 1$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{v - 6}{v - 6}$ by cancelling the common factors.

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Step 1.1.1

Cancel the common factor.

$\frac{v - 6}{v - 6} = \frac{v - 4}{v - 1} - 1$

Step 1.1.2

Rewrite the expression.

$\frac{1}{1} = \frac{v - 4}{v - 1} - 1$

Step 1.2

Rewrite the expression.

$1 = \frac{v - 4}{v - 1} - 1$

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.

$1, v - 1, 1$

Step 2.2

Remove parentheses.

$1, v - 1, 1$

Step 2.3

The LCM of one and any expression is the expression.

$v - 1$

Step 3

Multiply each term in $1 = \frac{v - 4}{v - 1} - 1$ by $v - 1$ to eliminate the fractions.

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Step 3.1

Multiply each term in $1 = \frac{v - 4}{v - 1} - 1$ by $v - 1$ .

$1 (v - 1) = \frac{v - 4}{v - 1} (v - 1) - (v - 1)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Multiply $v - 1$ by $1$ .

$v - 1 = \frac{v - 4}{v - 1} (v - 1) - (v - 1)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $v - 1$ .

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Step 3.3.1.1.1

Cancel the common factor.

$v - 1 = \frac{v - 4}{v - 1} (v - 1) - (v - 1)$

Step 3.3.1.1.2

Rewrite the expression.

$v - 1 = v - 4 - (v - 1)$

Step 3.3.1.2

Apply the distributive property.

$v - 1 = v - 4 - v - - 1$

Step 3.3.1.3

Multiply $- 1$ by $- 1$ .

$v - 1 = v - 4 - v + 1$

Step 3.3.2

Simplify by adding terms.

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Step 3.3.2.1

Combine the opposite terms in $v - 4 - v + 1$ .

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Step 3.3.2.1.1

Subtract $v$ from $v$ .

$v - 1 = 0 - 4 + 1$

Step 3.3.2.1.2

Subtract $4$ from $0$ .

$v - 1 = - 4 + 1$

Step 3.3.2.2

Add $- 4$ and $1$ .

$v - 1 = - 3$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$v = - 3 + 1$

Step 4.2

Add $- 3$ and $1$ .

$v = - 2$