Algebra Examples

$\frac{3 + 4 n}{n} = 7 b$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$n, 1$

Step 1.2

The LCM of one and any expression is the expression.

$n$

Step 2

Multiply each term in $\frac{3 + 4 n}{n} = 7 b$ by $n$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{3 + 4 n}{n} = 7 b$ by $n$ .

$\frac{3 + 4 n}{n} n = 7 b n$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $n$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 + 4 n}{n} n = 7 b n$

Step 2.2.1.2

Rewrite the expression.

$3 + 4 n = 7 b n$

Step 3

Solve the equation.

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Step 3.1

Subtract $7 b n$ from both sides of the equation.

$3 + 4 n - 7 b n = 0$

Step 3.2

Subtract $3$ from both sides of the equation.

$4 n - 7 b n = - 3$

Step 3.3

Factor $n$ out of $4 n - 7 b n$ .

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Step 3.3.1

Factor $n$ out of $4 n$ .

$n \cdot 4 - 7 b n = - 3$

Step 3.3.2

Factor $n$ out of $- 7 b n$ .

$n \cdot 4 + n (- 7 b) = - 3$

Step 3.3.3

Factor $n$ out of $n \cdot 4 + n (- 7 b)$ .

$n (4 - 7 b) = - 3$

Step 3.4

Divide each term in $n (4 - 7 b) = - 3$ by $4 - 7 b$ and simplify.

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Step 3.4.1

Divide each term in $n (4 - 7 b) = - 3$ by $4 - 7 b$ .

$\frac{n (4 - 7 b)}{4 - 7 b} = \frac{- 3}{4 - 7 b}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $4 - 7 b$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{n (4 - 7 b)}{4 - 7 b} = \frac{- 3}{4 - 7 b}$

Step 3.4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 3}{4 - 7 b}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Move the negative in front of the fraction.

$n = - \frac{3}{4 - 7 b}$