Basic Math Examples

$\frac{6 y - 6}{y} \div \frac{8 y - 8}{7 y^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 y - 6}{y} \cdot \frac{7 y^{2}}{8 y - 8}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y$ .

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Step 2.1.1

Factor $y$ out of $7 y^{2}$ .

$\frac{6 y - 6}{y} \cdot \frac{y (7 y)}{8 y - 8}$

Step 2.1.2

Cancel the common factor.

$\frac{6 y - 6}{y} \cdot \frac{y (7 y)}{8 y - 8}$

Step 2.1.3

Rewrite the expression.

$(6 y - 6) \frac{7 y}{8 y - 8}$

$(6 y - 6) \frac{7 y}{8 y - 8}$

Step 2.2

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

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Step 2.2.1

Factor $8$ out of $8 y$ .

$(6 y - 6) \frac{7 y}{8 (y) - 8}$

Step 2.2.2

Factor $8$ out of $- 8$ .

$(6 y - 6) \frac{7 y}{8 (y) + 8 (- 1)}$

Step 2.2.3

Factor $8$ out of $8 (y) + 8 (- 1)$ .

$(6 y - 6) \frac{7 y}{8 (y - 1)}$

$(6 y - 6) \frac{7 y}{8 (y - 1)}$

Step 2.3

Multiply $6 y - 6$ by $\frac{7 y}{8 (y - 1)}$ .

$\frac{(6 y - 6) (7 y)}{8 (y - 1)}$

Step 2.4

Cancel the common factor of $6 y - 6$ and $8$ .

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Step 2.4.1

Factor $2$ out of $(6 y - 6) (7 y)$ .

$\frac{2 ((3 y - 3) (7 y))}{8 (y - 1)}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $8 (y - 1)$ .

$\frac{2 ((3 y - 3) (7 y))}{2 (4 (y - 1))}$

Step 2.4.2.2

Cancel the common factor.

$\frac{2 ((3 y - 3) (7 y))}{2 (4 (y - 1))}$

Step 2.4.2.3

Rewrite the expression.

$\frac{(3 y - 3) (7 y)}{4 (y - 1)}$

$\frac{(3 y - 3) (7 y)}{4 (y - 1)}$

$\frac{(3 y - 3) (7 y)}{4 (y - 1)}$

$\frac{(3 y - 3) (7 y)}{4 (y - 1)}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $3$ out of $3 y - 3$ .

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Step 3.1.1

Factor $3$ out of $3 y$ .

$\frac{(3 (y) - 3) \cdot 7 y}{4 (y - 1)}$

Step 3.1.2

Factor $3$ out of $- 3$ .

$\frac{(3 (y) + 3 (- 1)) \cdot 7 y}{4 (y - 1)}$

Step 3.1.3

Factor $3$ out of $3 (y) + 3 (- 1)$ .

$\frac{3 (y - 1) \cdot 7 y}{4 (y - 1)}$

$\frac{3 (y - 1) \cdot 7 y}{4 (y - 1)}$

Step 3.2

Multiply $7$ by $3$ .

$\frac{21 (y - 1) y}{4 (y - 1)}$

$\frac{21 (y - 1) y}{4 (y - 1)}$

Step 4

Cancel the common factor of $y - 1$ .

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Step 4.1

Cancel the common factor.

$\frac{21 (y - 1) y}{4 (y - 1)}$

Step 4.2

Rewrite the expression.

$\frac{21 y}{4}$

$\frac{21 y}{4}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$