Basic Math Examples

$\frac{3 y^{3} - 4}{4 y^{4}} - \frac{7 y^{3} - 4}{4 y^{4}}$

Step 1

Combine the numerators over the common denominator.

$\frac{3 y^{3} - 4 - (7 y^{3} - 4)}{4 y^{4}}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{3 y^{3} - 4 - (7 y^{3}) - - 4}{4 y^{4}}$

Step 2.2

Multiply $7$ by $- 1$ .

$\frac{3 y^{3} - 4 - 7 y^{3} - - 4}{4 y^{4}}$

Step 2.3

Multiply $- 1$ by $- 4$ .

$\frac{3 y^{3} - 4 - 7 y^{3} + 4}{4 y^{4}}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $3 y^{3} - 4 - 7 y^{3} + 4$ .

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Step 3.1.1

Add $- 4$ and $4$ .

$\frac{3 y^{3} - 7 y^{3} + 0}{4 y^{4}}$

Step 3.1.2

Add $3 y^{3} - 7 y^{3}$ and $0$ .

$\frac{3 y^{3} - 7 y^{3}}{4 y^{4}}$

Step 3.2

Subtract $7 y^{3}$ from $3 y^{3}$ .

$\frac{- 4 y^{3}}{4 y^{4}}$

Step 3.3

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

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Step 3.3.1

Factor $4$ out of $- 4 y^{3}$ .

$\frac{4 (- y^{3})}{4 y^{4}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $4$ out of $4 y^{4}$ .

$\frac{4 (- y^{3})}{4 (y^{4})}$

Step 3.3.2.2

Cancel the common factor.

$\frac{4 (- y^{3})}{4 y^{4}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{- y^{3}}{y^{4}}$

Step 3.4

Cancel the common factor of $y^{3}$ and $y^{4}$ .

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Step 3.4.1

Factor $y^{3}$ out of $- y^{3}$ .

$\frac{y^{3} \cdot - 1}{y^{4}}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $y^{3}$ out of $y^{4}$ .

$\frac{y^{3} \cdot - 1}{y^{3} y}$

Step 3.4.2.2

Cancel the common factor.

$\frac{y^{3} \cdot - 1}{y^{3} y}$

Step 3.4.2.3

Rewrite the expression.

$\frac{- 1}{y}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{1}{y}$