Algebra Examples

$\frac{- 6 y^{2}}{8 y + 5} + \frac{3}{y^{4}}$

Step 1

Move the negative in front of the fraction.

$- \frac{6 y^{2}}{8 y + 5} + \frac{3}{y^{4}}$

Step 2

To write $- \frac{6 y^{2}}{8 y + 5}$ as a fraction with a common denominator, multiply by $\frac{y^{4}}{y^{4}}$ .

$- \frac{6 y^{2}}{8 y + 5} \cdot \frac{y^{4}}{y^{4}} + \frac{3}{y^{4}}$

Step 3

To write $\frac{3}{y^{4}}$ as a fraction with a common denominator, multiply by $\frac{8 y + 5}{8 y + 5}$ .

$- \frac{6 y^{2}}{8 y + 5} \cdot \frac{y^{4}}{y^{4}} + \frac{3}{y^{4}} \cdot \frac{8 y + 5}{8 y + 5}$

Step 4

Write each expression with a common denominator of $(8 y + 5) y^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6 y^{2}}{8 y + 5}$ by $\frac{y^{4}}{y^{4}}$ .

$- \frac{6 y^{2} y^{4}}{(8 y + 5) y^{4}} + \frac{3}{y^{4}} \cdot \frac{8 y + 5}{8 y + 5}$

Step 4.2

Multiply $\frac{3}{y^{4}}$ by $\frac{8 y + 5}{8 y + 5}$ .

$- \frac{6 y^{2} y^{4}}{(8 y + 5) y^{4}} + \frac{3 (8 y + 5)}{y^{4} (8 y + 5)}$

Step 4.3

Reorder the factors of $(8 y + 5) y^{4}$ .

$- \frac{6 y^{2} y^{4}}{y^{4} (8 y + 5)} + \frac{3 (8 y + 5)}{y^{4} (8 y + 5)}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 6 y^{2} y^{4} + 3 (8 y + 5)}{y^{4} (8 y + 5)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $3$ out of $- 6 y^{2} y^{4} + 3 (8 y + 5)$ .

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Step 6.1.1

Factor $3$ out of $- 6 y^{2} y^{4}$ .

$\frac{3 (- 2 y^{2} y^{4}) + 3 (8 y + 5)}{y^{4} (8 y + 5)}$

Step 6.1.2

Factor $3$ out of $3 (- 2 y^{2} y^{4}) + 3 (8 y + 5)$ .

$\frac{3 (- 2 y^{2} y^{4} + 8 y + 5)}{y^{4} (8 y + 5)}$

Step 6.2

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

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Step 6.2.1

Move $y^{4}$ .

$\frac{3 (- 2 (y^{4} y^{2}) + 8 y + 5)}{y^{4} (8 y + 5)}$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 (- 2 y^{4 + 2} + 8 y + 5)}{y^{4} (8 y + 5)}$

Step 6.2.3

Add $4$ and $2$ .

$\frac{3 (- 2 y^{6} + 8 y + 5)}{y^{4} (8 y + 5)}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 2 y^{6}$ .

$\frac{3 (- (2 y^{6}) + 8 y + 5)}{y^{4} (8 y + 5)}$

Step 7.2

Factor $- 1$ out of $8 y$ .

$\frac{3 (- (2 y^{6}) - (- 8 y) + 5)}{y^{4} (8 y + 5)}$

Step 7.3

Factor $- 1$ out of $- (2 y^{6}) - (- 8 y)$ .

$\frac{3 (- (2 y^{6} - 8 y) + 5)}{y^{4} (8 y + 5)}$

Step 7.4

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{3 (- (2 y^{6} - 8 y) - 1 (- 5))}{y^{4} (8 y + 5)}$

Step 7.5

Factor $- 1$ out of $- (2 y^{6} - 8 y) - 1 (- 5)$ .

$\frac{3 (- (2 y^{6} - 8 y - 5))}{y^{4} (8 y + 5)}$

Step 7.6

Simplify the expression.

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Step 7.6.1

Rewrite $- (2 y^{6} - 8 y - 5)$ as $- 1 (2 y^{6} - 8 y - 5)$ .

$\frac{3 (- 1 (2 y^{6} - 8 y - 5))}{y^{4} (8 y + 5)}$

Step 7.6.2

Move the negative in front of the fraction.

$- \frac{3 (2 y^{6} - 8 y - 5)}{y^{4} (8 y + 5)}$