Basic Math Examples

$l = \frac{K + 1}{k} - \frac{m + 1}{m}$

Step 1

Rewrite the equation as $\frac{K + 1}{k} - \frac{m + 1}{m} = l$ .

$\frac{K + 1}{k} - \frac{m + 1}{m} = l$

Step 2

Simplify $\frac{K + 1}{k} - \frac{m + 1}{m}$ .

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Step 2.1

To write $\frac{K + 1}{k}$ as a fraction with a common denominator, multiply by $\frac{m}{m}$ .

$\frac{K + 1}{k} \cdot \frac{m}{m} - \frac{m + 1}{m} = l$

Step 2.2

To write $- \frac{m + 1}{m}$ as a fraction with a common denominator, multiply by $\frac{k}{k}$ .

$\frac{K + 1}{k} \cdot \frac{m}{m} - \frac{m + 1}{m} \cdot \frac{k}{k} = l$

Step 2.3

Write each expression with a common denominator of $k m$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{K + 1}{k}$ by $\frac{m}{m}$ .

$\frac{(K + 1) m}{k m} - \frac{m + 1}{m} \cdot \frac{k}{k} = l$

Step 2.3.2

Multiply $\frac{m + 1}{m}$ by $\frac{k}{k}$ .

$\frac{(K + 1) m}{k m} - \frac{(m + 1) k}{m k} = l$

Step 2.3.3

Reorder the factors of $m k$ .

$\frac{(K + 1) m}{k m} - \frac{(m + 1) k}{k m} = l$

Step 2.4

Combine the numerators over the common denominator.

$\frac{(K + 1) m - (m + 1) k}{k m} = l$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{K m + 1 m - (m + 1) k}{k m} = l$

Step 2.5.2

Multiply $m$ by $1$ .

$\frac{K m + m - (m + 1) k}{k m} = l$

Step 2.5.3

Apply the distributive property.

$\frac{K m + m + (- m - 1 \cdot 1) k}{k m} = l$

Step 2.5.4

Multiply $- 1$ by $1$ .

$\frac{K m + m + (- m - 1) k}{k m} = l$

Step 2.5.5

Apply the distributive property.

$\frac{K m + m - m k - 1 k}{k m} = l$

Step 2.5.6

Rewrite $- 1 k$ as $- k$ .

$\frac{K m + m - m k - k}{k m} = l$

Step 3

Multiply both sides by $k m$ .

$\frac{K m + m - m k - k}{k m} (k m) = l (k m)$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{K m + m - m k - k}{k m} (k m)$ .

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Step 4.1.1.1

Cancel the common factor of $k m$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{K m + m - m k - k}{k m} (k m) = l (k m)$

Step 4.1.1.1.2

Rewrite the expression.

$K m + m - m k - k = l (k m)$

Step 4.1.1.2

Reorder.

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Step 4.1.1.2.1

Move $m$ .

$K m + m - 1 k m - k = l (k m)$

Step 4.1.1.2.2

Move $m$ .

$K m - 1 k m - k + m = l (k m)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Remove parentheses.

$K m - 1 k m - k + m = l k m$

Step 5

Solve for $K$ .

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Step 5.1

Rewrite $- 1 k$ as $- k$ .

$K m - k m - k + m = l k m$

Step 5.2

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

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Step 5.2.1

Add $k m$ to both sides of the equation.

$K m - k + m = l k m + k m$

Step 5.2.2

Add $k$ to both sides of the equation.

$K m + m = l k m + k m + k$

Step 5.2.3

Subtract $m$ from both sides of the equation.

$K m = l k m + k m + k - m$

Step 5.3

Divide each term in $K m = l k m + k m + k - m$ by $m$ and simplify.

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Step 5.3.1

Divide each term in $K m = l k m + k m + k - m$ by $m$ .

$\frac{K m}{m} = \frac{l k m}{m} + \frac{k m}{m} + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $m$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{K m}{m} = \frac{l k m}{m} + \frac{k m}{m} + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.2.1.2

Divide $K$ by $1$ .

$K = \frac{l k m}{m} + \frac{k m}{m} + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Simplify each term.

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Step 5.3.3.1.1

Cancel the common factor of $m$ .

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Step 5.3.3.1.1.1

Cancel the common factor.

$K = \frac{l k m}{m} + \frac{k m}{m} + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.3.1.1.2

Divide $l k$ by $1$ .

$K = l k + \frac{k m}{m} + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.3.1.2

Cancel the common factor of $m$ .

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Step 5.3.3.1.2.1

Cancel the common factor.

$K = l k + \frac{k m}{m} + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.3.1.2.2

Divide $k$ by $1$ .

$K = l k + k + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.3.1.3

Cancel the common factor of $m$ .

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Step 5.3.3.1.3.1

Cancel the common factor.

$K = l k + k + \frac{k}{m} + \frac{- m}{m}$

Step 5.3.3.1.3.2

Divide $- 1$ by $1$ .

$K = l k + k + \frac{k}{m} - 1$