Algebra Examples

$m - n - \frac{n^{2}}{m + n}$

Step 1

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

$- n + \frac{m (m + n)}{m + n} - \frac{n^{2}}{m + n}$

Step 2

Combine the numerators over the common denominator.

$- n + \frac{m (m + n) - n^{2}}{m + n}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$- n + \frac{m \cdot m + m n - n^{2}}{m + n}$

Step 3.2

Multiply $m$ by $m$ .

$- n + \frac{m^{2} + m n - n^{2}}{m + n}$

Step 4

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

$- n \cdot \frac{m + n}{m + n} + \frac{m^{2} + m n - n^{2}}{m + n}$

Step 5

Simplify terms.

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Step 5.1

Combine $- n$ and $\frac{m + n}{m + n}$ .

$\frac{- n (m + n)}{m + n} + \frac{m^{2} + m n - n^{2}}{m + n}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{- n (m + n) + m^{2} + m n - n^{2}}{m + n}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{- n m - n \cdot n + m^{2} + m n - n^{2}}{m + n}$

Step 6.2

Multiply $n$ by $n$ by adding the exponents.

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Step 6.2.1

Move $n$ .

$\frac{- n m - (n \cdot n) + m^{2} + m n - n^{2}}{m + n}$

Step 6.2.2

Multiply $n$ by $n$ .

$\frac{- n m - n^{2} + m^{2} + m n - n^{2}}{m + n}$

Step 6.3

Add $- n m$ and $m n$ .

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Step 6.3.1

Move $n$ .

$\frac{- n^{2} + m^{2} - m n + m n - n^{2}}{m + n}$

Step 6.3.2

Add $- m n$ and $m n$ .

$\frac{- n^{2} + m^{2} + 0 - n^{2}}{m + n}$

Step 6.4

Add $- n^{2}$ and $0$ .

$\frac{m^{2} - n^{2} - n^{2}}{m + n}$

Step 6.5

Subtract $n^{2}$ from $- n^{2}$ .

$\frac{m^{2} - 2 n^{2}}{m + n}$