Basic Math Examples

$9 y - \frac{18}{8 y - 16}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $18$ and $8 y - 16$ .

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Step 1.1.1

Factor $2$ out of $18$ .

$9 y - \frac{2 (9)}{8 y - 16}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $8 y$ .

$9 y - \frac{2 (9)}{2 (4 y) - 16}$

Step 1.1.2.2

Factor $2$ out of $- 16$ .

$9 y - \frac{2 \cdot 9}{2 (4 y) + 2 \cdot - 8}$

Step 1.1.2.3

Factor $2$ out of $2 (4 y) + 2 (- 8)$ .

$9 y - \frac{2 (9)}{2 (4 y - 8)}$

Step 1.1.2.4

Cancel the common factor.

$9 y - \frac{2 \cdot 9}{2 (4 y - 8)}$

Step 1.1.2.5

Rewrite the expression.

$9 y - \frac{9}{4 y - 8}$

Step 1.2

Factor $4$ out of $4 y - 8$ .

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Step 1.2.1

Factor $4$ out of $4 y$ .

$9 y - \frac{9}{4 (y) - 8}$

Step 1.2.2

Factor $4$ out of $- 8$ .

$9 y - \frac{9}{4 y + 4 \cdot - 2}$

Step 1.2.3

Factor $4$ out of $4 y + 4 \cdot - 2$ .

$9 y - \frac{9}{4 (y - 2)}$

Step 2

To write $9 y$ as a fraction with a common denominator, multiply by $\frac{4 (y - 2)}{4 (y - 2)}$ .

$9 y \cdot \frac{4 (y - 2)}{4 (y - 2)} - \frac{9}{4 (y - 2)}$

Step 3

Simplify terms.

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Step 3.1

Combine $9 y$ and $\frac{4 (y - 2)}{4 (y - 2)}$ .

$\frac{9 y (4 (y - 2))}{4 (y - 2)} - \frac{9}{4 (y - 2)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{9 y (4 (y - 2)) - 9}{4 (y - 2)}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $9$ out of $9 y (4 (y - 2)) - 9$ .

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Step 4.1.1

Factor $9$ out of $9 y (4 (y - 2))$ .

$\frac{9 (y (4 (y - 2))) - 9}{4 (y - 2)}$

Step 4.1.2

Factor $9$ out of $- 9$ .

$\frac{9 (y (4 (y - 2))) + 9 (- 1)}{4 (y - 2)}$

Step 4.1.3

Factor $9$ out of $9 (y (4 (y - 2))) + 9 (- 1)$ .

$\frac{9 (y (4 (y - 2)) - 1)}{4 (y - 2)}$

Step 4.2

Rewrite using the commutative property of multiplication.

$\frac{9 (4 y (y - 2) - 1)}{4 (y - 2)}$

Step 4.3

Apply the distributive property.

$\frac{9 (4 y \cdot y + 4 y \cdot - 2 - 1)}{4 (y - 2)}$

Step 4.4

Multiply $y$ by $y$ by adding the exponents.

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Step 4.4.1

Move $y$ .

$\frac{9 (4 (y \cdot y) + 4 y \cdot - 2 - 1)}{4 (y - 2)}$

Step 4.4.2

Multiply $y$ by $y$ .

$\frac{9 (4 y^{2} + 4 y \cdot - 2 - 1)}{4 (y - 2)}$

Step 4.5

Multiply $- 2$ by $4$ .

$\frac{9 (4 y^{2} - 8 y - 1)}{4 (y - 2)}$