Pre-Algebra Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $m p$ .

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Step 1.1

Multiply $\frac{\frac{5}{m p} - \frac{9}{p} + \frac{3}{m}}{2 m^{- 1} - 5 p^{- 1}}$ by $\frac{m p}{m p}$ .

$\frac{m p}{m p} \cdot \frac{\frac{5}{m p} - \frac{9}{p} + \frac{3}{m}}{2 m^{- 1} - 5 p^{- 1}}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $m p$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $p$ .

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Step 3.2.1

Move the leading negative in $- \frac{9}{p}$ into the numerator.

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

Step 3.2.2

Factor $p$ out of $m p$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.3

Cancel the common factor of $m$ .

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Step 3.3.1

Factor $m$ out of $m p$ .

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

Step 3.3.2

Cancel the common factor.

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

Step 3.3.3

Rewrite the expression.

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

Step 4

Simplify the numerator.

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Step 4.1

Move $- 9$ to the left of $m$ .

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

Step 4.2

Move $3$ to the left of $p$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Rewrite using the commutative property of multiplication.

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

Step 5.2

Multiply $m$ by $m^{- 1}$ by adding the exponents.

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Step 5.2.1

Move $m^{- 1}$ .

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

Step 5.2.2

Multiply $m^{- 1}$ by $m$ .

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Step 5.2.2.1

Raise $m$ to the power of $1$ .

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

Step 5.2.2.2

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

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

Step 5.2.3

Add $- 1$ and $1$ .

$\frac{5 - 9 m + 3 p}{2 m^{0} p + m p (- 5 p^{- 1})}$

Step 5.3

Simplify $2 m^{0} p$ .

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

Step 5.4

Rewrite using the commutative property of multiplication.

$\frac{5 - 9 m + 3 p}{2 p - 5 m p \cdot p^{- 1}}$

Step 5.5

Multiply $p$ by $p^{- 1}$ by adding the exponents.

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Step 5.5.1

Move $p^{- 1}$ .

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

Step 5.5.2

Multiply $p^{- 1}$ by $p$ .

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Step 5.5.2.1

Raise $p$ to the power of $1$ .

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

Step 5.5.2.2

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

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

Step 5.5.3

Add $- 1$ and $1$ .

$\frac{5 - 9 m + 3 p}{2 p - 5 m p^{0}}$

Step 5.6

Simplify $- 5 m p^{0}$ .

$\frac{5 - 9 m + 3 p}{2 p - 5 m}$

Step 6

Split the fraction $\frac{5 - 9 m + 3 p}{2 p - 5 m}$ into two fractions.

$\frac{5 - 9 m}{2 p - 5 m} + \frac{3 p}{2 p - 5 m}$

Step 7

Split the fraction $\frac{5 - 9 m}{2 p - 5 m}$ into two fractions.

$\frac{5}{2 p - 5 m} + \frac{- 9 m}{2 p - 5 m} + \frac{3 p}{2 p - 5 m}$

Step 8

Move the negative in front of the fraction.

$\frac{5}{2 p - 5 m} - \frac{9 m}{2 p - 5 m} + \frac{3 p}{2 p - 5 m}$