Basic Math Examples

$\frac{\frac{49 y + 21}{6 y}}{\frac{42 y + 18}{6}}$

Step 1

Cancel the common factor of $42 y + 18$ and $6$ .

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Step 1.1

Factor $6$ out of $42 y$ .

$\frac{\frac{49 y + 21}{6 y}}{\frac{6 (7 y) + 18}{6}}$

Step 1.2

Factor $6$ out of $18$ .

$\frac{\frac{49 y + 21}{6 y}}{\frac{6 (7 y) + 6 \cdot 3}{6}}$

Step 1.3

Factor $6$ out of $6 (7 y) + 6 (3)$ .

$\frac{\frac{49 y + 21}{6 y}}{\frac{6 (7 y + 3)}{6}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $6$ out of $6$ .

$\frac{\frac{49 y + 21}{6 y}}{\frac{6 (7 y + 3)}{6 (1)}}$

Step 1.4.2

Cancel the common factor.

$\frac{\frac{49 y + 21}{6 y}}{\frac{6 (7 y + 3)}{6 \cdot 1}}$

Step 1.4.3

Rewrite the expression.

$\frac{\frac{49 y + 21}{6 y}}{\frac{7 y + 3}{1}}$

Step 1.4.4

Divide $7 y + 3$ by $1$ .

$\frac{\frac{49 y + 21}{6 y}}{7 y + 3}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{49 y + 21}{6 y} \cdot \frac{1}{7 y + 3}$

Step 3

Factor $7$ out of $49 y + 21$ .

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Step 3.1

Factor $7$ out of $49 y$ .

$\frac{7 (7 y) + 21}{6 y} \cdot \frac{1}{7 y + 3}$

Step 3.2

Factor $7$ out of $21$ .

$\frac{7 (7 y) + 7 (3)}{6 y} \cdot \frac{1}{7 y + 3}$

Step 3.3

Factor $7$ out of $7 (7 y) + 7 (3)$ .

$\frac{7 (7 y + 3)}{6 y} \cdot \frac{1}{7 y + 3}$

Step 4

Cancel the common factor of $7 y + 3$ .

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Step 4.1

Factor $7 y + 3$ out of $7 (7 y + 3)$ .

$\frac{(7 y + 3) \cdot 7}{6 y} \cdot \frac{1}{7 y + 3}$

Step 4.2

Cancel the common factor.

$\frac{(7 y + 3) \cdot 7}{6 y} \cdot \frac{1}{7 y + 3}$

Step 4.3

Rewrite the expression.

$\frac{7}{6 y}$