Algebra Examples

$\frac{16 m^{4} - 12 m^{3} + 4 m^{2} + 8 m - 9}{4 m^{2}}$

Step 1

Split the fraction $\frac{16 m^{4} - 12 m^{3} + 4 m^{2} + 8 m - 9}{4 m^{2}}$ into two fractions.

$\frac{16 m^{4} - 12 m^{3} + 4 m^{2} + 8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 2

Split the fraction $\frac{16 m^{4} - 12 m^{3} + 4 m^{2} + 8 m}{4 m^{2}}$ into two fractions.

$\frac{16 m^{4} - 12 m^{3} + 4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 3

Split the fraction $\frac{16 m^{4} - 12 m^{3} + 4 m^{2}}{4 m^{2}}$ into two fractions.

$\frac{16 m^{4} - 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 4

Split the fraction $\frac{16 m^{4} - 12 m^{3}}{4 m^{2}}$ into two fractions.

$\frac{16 m^{4}}{4 m^{2}} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 5

Cancel the common factor of $16$ and $4$ .

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Step 5.1

Factor $4$ out of $16 m^{4}$ .

$\frac{4 (4 m^{4})}{4 m^{2}} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $4$ out of $4 m^{2}$ .

$\frac{4 (4 m^{4})}{4 (m^{2})} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 5.2.2

Cancel the common factor.

$\frac{4 (4 m^{4})}{4 m^{2}} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 5.2.3

Rewrite the expression.

$\frac{4 m^{4}}{m^{2}} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 6

Cancel the common factor of $m^{4}$ and $m^{2}$ .

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Step 6.1

Factor $m^{2}$ out of $4 m^{4}$ .

$\frac{m^{2} (4 m^{2})}{m^{2}} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Multiply by $1$ .

$\frac{m^{2} (4 m^{2})}{m^{2} \cdot 1} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 6.2.2

Cancel the common factor.

$\frac{m^{2} (4 m^{2})}{m^{2} \cdot 1} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 6.2.3

Rewrite the expression.

$\frac{4 m^{2}}{1} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 6.2.4

Divide $4 m^{2}$ by $1$ .

$4 m^{2} + \frac{- 12 m^{3}}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 7

Cancel the common factor of $- 12$ and $4$ .

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Step 7.1

Factor $4$ out of $- 12 m^{3}$ .

$4 m^{2} + \frac{4 (- 3 m^{3})}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $4$ out of $4 m^{2}$ .

$4 m^{2} + \frac{4 (- 3 m^{3})}{4 (m^{2})} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 7.2.2

Cancel the common factor.

$4 m^{2} + \frac{4 (- 3 m^{3})}{4 m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 7.2.3

Rewrite the expression.

$4 m^{2} + \frac{- 3 m^{3}}{m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 8

Cancel the common factor of $m^{3}$ and $m^{2}$ .

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Step 8.1

Factor $m^{2}$ out of $- 3 m^{3}$ .

$4 m^{2} + \frac{m^{2} (- 3 m)}{m^{2}} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Multiply by $1$ .

$4 m^{2} + \frac{m^{2} (- 3 m)}{m^{2} \cdot 1} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 8.2.2

Cancel the common factor.

$4 m^{2} + \frac{m^{2} (- 3 m)}{m^{2} \cdot 1} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 8.2.3

Rewrite the expression.

$4 m^{2} + \frac{- 3 m}{1} + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 8.2.4

Divide $- 3 m$ by $1$ .

$4 m^{2} - 3 m + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 9

Cancel the common factor of $4$ .

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Step 9.1

Cancel the common factor.

$4 m^{2} - 3 m + \frac{4 m^{2}}{4 m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 9.2

Rewrite the expression.

$4 m^{2} - 3 m + \frac{m^{2}}{m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 10

Cancel the common factor of $m^{2}$ .

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Step 10.1

Cancel the common factor.

$4 m^{2} - 3 m + \frac{m^{2}}{m^{2}} + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 10.2

Rewrite the expression.

$4 m^{2} - 3 m + 1 + \frac{8 m}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 11

Cancel the common factor of $8$ and $4$ .

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Step 11.1

Factor $4$ out of $8 m$ .

$4 m^{2} - 3 m + 1 + \frac{4 (2 m)}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $4$ out of $4 m^{2}$ .

$4 m^{2} - 3 m + 1 + \frac{4 (2 m)}{4 (m^{2})} + \frac{- 9}{4 m^{2}}$

Step 11.2.2

Cancel the common factor.

$4 m^{2} - 3 m + 1 + \frac{4 (2 m)}{4 m^{2}} + \frac{- 9}{4 m^{2}}$

Step 11.2.3

Rewrite the expression.

$4 m^{2} - 3 m + 1 + \frac{2 m}{m^{2}} + \frac{- 9}{4 m^{2}}$

Step 12

Cancel the common factor of $m$ and $m^{2}$ .

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Step 12.1

Factor $m$ out of $2 m$ .

$4 m^{2} - 3 m + 1 + \frac{m \cdot 2}{m^{2}} + \frac{- 9}{4 m^{2}}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $m$ out of $m^{2}$ .

$4 m^{2} - 3 m + 1 + \frac{m \cdot 2}{m \cdot m} + \frac{- 9}{4 m^{2}}$

Step 12.2.2

Cancel the common factor.

$4 m^{2} - 3 m + 1 + \frac{m \cdot 2}{m \cdot m} + \frac{- 9}{4 m^{2}}$

Step 12.2.3

Rewrite the expression.

$4 m^{2} - 3 m + 1 + \frac{2}{m} + \frac{- 9}{4 m^{2}}$

Step 13

Move the negative in front of the fraction.

$4 m^{2} - 3 m + 1 + \frac{2}{m} - \frac{9}{4 m^{2}}$