Basic Math Examples

$\frac{6 p - 6}{p} + \frac{10 p - 10}{9 p^{2}}$

Step 1

Simplify each term.

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Step 1.1

Factor $6$ out of $6 p - 6$ .

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Step 1.1.1

Factor $6$ out of $6 p$ .

$\frac{6 (p) - 6}{p} + \frac{10 p - 10}{9 p^{2}}$

Step 1.1.2

Factor $6$ out of $- 6$ .

$\frac{6 (p) + 6 (- 1)}{p} + \frac{10 p - 10}{9 p^{2}}$

Step 1.1.3

Factor $6$ out of $6 (p) + 6 (- 1)$ .

$\frac{6 (p - 1)}{p} + \frac{10 p - 10}{9 p^{2}}$

Step 1.2

Factor $10$ out of $10 p - 10$ .

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Step 1.2.1

Factor $10$ out of $10 p$ .

$\frac{6 (p - 1)}{p} + \frac{10 (p) - 10}{9 p^{2}}$

Step 1.2.2

Factor $10$ out of $- 10$ .

$\frac{6 (p - 1)}{p} + \frac{10 (p) + 10 (- 1)}{9 p^{2}}$

Step 1.2.3

Factor $10$ out of $10 (p) + 10 (- 1)$ .

$\frac{6 (p - 1)}{p} + \frac{10 (p - 1)}{9 p^{2}}$

Step 2

To write $\frac{6 (p - 1)}{p}$ as a fraction with a common denominator, multiply by $\frac{9 p}{9 p}$ .

$\frac{6 (p - 1)}{p} \cdot \frac{9 p}{9 p} + \frac{10 (p - 1)}{9 p^{2}}$

Step 3

Write each expression with a common denominator of $9 p^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6 (p - 1)}{p}$ by $\frac{9 p}{9 p}$ .

$\frac{6 (p - 1) (9 p)}{p (9 p)} + \frac{10 (p - 1)}{9 p^{2}}$

Step 3.2

Rewrite using the commutative property of multiplication.

$\frac{6 (p - 1) (9 p)}{9 p \cdot p} + \frac{10 (p - 1)}{9 p^{2}}$

Step 3.3

Multiply $p$ by $p$ by adding the exponents.

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Step 3.3.1

Move $p$ .

$\frac{6 (p - 1) (9 p)}{9 (p \cdot p)} + \frac{10 (p - 1)}{9 p^{2}}$

Step 3.3.2

Multiply $p$ by $p$ .

$\frac{6 (p - 1) (9 p)}{9 p^{2}} + \frac{10 (p - 1)}{9 p^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (p - 1) (9 p) + 10 (p - 1)}{9 p^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $2 (p - 1)$ out of $6 (p - 1) (9 p) + 10 (p - 1)$ .

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Step 5.1.1

Factor $2 (p - 1)$ out of $6 (p - 1) (9 p)$ .

$\frac{2 (p - 1) (3 (9 p)) + 10 (p - 1)}{9 p^{2}}$

Step 5.1.2

Factor $2 (p - 1)$ out of $10 (p - 1)$ .

$\frac{2 (p - 1) (3 (9 p)) + 2 (p - 1) (5)}{9 p^{2}}$

Step 5.1.3

Factor $2 (p - 1)$ out of $2 (p - 1) (3 (9 p)) + 2 (p - 1) (5)$ .

$\frac{2 (p - 1) (3 (9 p) + 5)}{9 p^{2}}$

Step 5.2

Multiply $9$ by $3$ .

$\frac{2 (p - 1) (27 p + 5)}{9 p^{2}}$