Basic Math Examples

$b + \frac{1}{c} = 1$

Step 1

Subtract $b$ from both sides of the equation.

$\frac{1}{c} = 1 - b$

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.

$c, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$c$

Step 3

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

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Step 3.1

Multiply each term in $\frac{1}{c} = 1 - b$ by $c$ .

$\frac{1}{c} c = 1 c - b c$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $c$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1}{c} c = 1 c - b c$

Step 3.2.1.2

Rewrite the expression.

$1 = 1 c - b c$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $c$ by $1$ .

$1 = c - b c$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $c - b c = 1$ .

$c - b c = 1$

Step 4.2

Factor $c$ out of $c - b c$ .

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Step 4.2.1

Factor $c$ out of $c^{1}$ .

$c \cdot 1 - b c = 1$

Step 4.2.2

Factor $c$ out of $- b c$ .

$c \cdot 1 + c (- b) = 1$

Step 4.2.3

Factor $c$ out of $c \cdot 1 + c (- b)$ .

$c (1 - b) = 1$

Step 4.3

Divide each term in $c (1 - b) = 1$ by $1 - b$ and simplify.

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Step 4.3.1

Divide each term in $c (1 - b) = 1$ by $1 - b$ .

$\frac{c (1 - b)}{1 - b} = \frac{1}{1 - b}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $1 - b$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{c (1 - b)}{1 - b} = \frac{1}{1 - b}$

Step 4.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{1}{1 - b}$