Basic Math Examples

$\frac{π}{π - q} - \frac{q}{q - π}$

Step 1

Factor $- 1$ out of $q$ .

$\frac{π}{π - q} - \frac{q}{- 1 (- q) - π}$

Step 2

Factor $- 1$ out of $- π$ .

$\frac{π}{π - q} - \frac{q}{- 1 (- q) - (π)}$

Step 3

Factor $- 1$ out of $- 1 (- q) - (π)$ .

$\frac{π}{π - q} - \frac{q}{- 1 (- q + π)}$

Step 4

Reorder terms.

$\frac{π}{- q + π} - \frac{q}{- 1 (- q + π)}$

Step 5

To write $\frac{π}{- q + π}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{π}{- q + π} \cdot \frac{- 1}{- 1} - \frac{q}{- 1 (- q + π)}$

Step 6

Write each expression with a common denominator of $(- q + π) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{π}{- q + π}$ by $\frac{- 1}{- 1}$ .

$\frac{π \cdot - 1}{(- q + π) \cdot - 1} - \frac{q}{- 1 (- q + π)}$

Step 6.2

Reorder the factors of $(- q + π) \cdot - 1$ .

$\frac{π \cdot - 1}{- (- q + π)} - \frac{q}{- 1 (- q + π)}$

Step 7

Combine the numerators over the common denominator.

$\frac{π \cdot - 1 - q}{- (- q + π)}$

Step 8

Simplify the numerator.

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Step 8.1

Move $- 1$ to the left of $π$ .

$\frac{- 1 \cdot π - q}{- (- q + π)}$

Step 8.2

Rewrite $- 1 π$ as $- π$ .

$\frac{- π - q}{- (- q + π)}$

Step 9

Simplify terms.

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Step 9.1

Move the negative in front of the fraction.

$- \frac{- π - q}{- q + π}$

Step 9.2

Factor $- 1$ out of $- π$ .

$- \frac{- (π) - q}{- q + π}$

Step 9.3

Factor $- 1$ out of $- q$ .

$- \frac{- (π) - (q)}{- q + π}$

Step 9.4

Factor $- 1$ out of $- (π) - (q)$ .

$- \frac{- (π + q)}{- q + π}$

Step 9.5

Rewrite $- (π + q)$ as $- 1 (π + q)$ .

$- \frac{- 1 (π + q)}{- q + π}$

Step 9.6

Factor $- 1$ out of $- q$ .

$- \frac{- 1 (π + q)}{- (q) + π}$

Step 9.7

Factor $- 1$ out of $π$ .

$- \frac{- 1 (π + q)}{- (q) - 1 (- π)}$

Step 9.8

Factor $- 1$ out of $- (q) - 1 (- π)$ .

$- \frac{- 1 (π + q)}{- (q - π)}$

Step 9.9

Rewrite $- (q - π)$ as $- 1 (q - π)$ .

$- \frac{- 1 (π + q)}{- 1 (q - π)}$

Step 9.10

Cancel the common factor.

$- \frac{- 1 (π + q)}{- 1 (q - π)}$

Step 9.11

Rewrite the expression.

$- \frac{π + q}{q - π}$