Calculus Examples

$P (7) = \frac{104 (7)}{(7) \cdot 9 x + 5}$

Step 1

Rewrite the equation as $\frac{104 (7)}{(7) \cdot (9 x) + 5} = P (7)$ .

$\frac{104 (7)}{(7) \cdot (9 x) + 5} = P (7)$

Step 2

Simplify $\frac{104 (7)}{(7) \cdot (9 x) + 5}$ .

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Step 2.1

Multiply $104$ by $7$ .

$\frac{728}{7 \cdot 9 x + 5} = P (7)$

Step 2.2

Multiply $7$ by $9$ .

$\frac{728}{63 x + 5} = P (7)$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$63 x + 5, 1$

Step 3.2

Remove parentheses.

$63 x + 5, 1$

Step 3.3

The LCM of one and any expression is the expression.

$63 x + 5$

Step 4

Multiply each term in $\frac{728}{63 x + 5} = P (7)$ by $63 x + 5$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{728}{63 x + 5} = P (7)$ by $63 x + 5$ .

$\frac{728}{63 x + 5} (63 x + 5) = P (7) (63 x + 5)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $63 x + 5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{728}{63 x + 5} (63 x + 5) = P (7) (63 x + 5)$

Step 4.2.1.2

Rewrite the expression.

$728 = P (7) (63 x + 5)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move $7$ to the left of $P$ .

$728 = 7 P (63 x + 5)$

Step 4.3.2

Apply the distributive property.

$728 = 7 P (63 x) + 7 P \cdot 5$

Step 4.3.3

Simplify the expression.

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Step 4.3.3.1

Rewrite using the commutative property of multiplication.

$728 = 7 \cdot 63 P x + 7 P \cdot 5$

Step 4.3.3.2

Multiply $5$ by $7$ .

$728 = 7 \cdot 63 P x + 35 P$

Step 4.3.3.3

Multiply $7$ by $63$ .

$728 = 441 P x + 35 P$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $441 P x + 35 P = 728$ .

$441 P x + 35 P = 728$

Step 5.2

Subtract $35 P$ from both sides of the equation.

$441 P x = 728 - 35 P$

Step 5.3

Divide each term in $441 P x = 728 - 35 P$ by $441 P$ and simplify.

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Step 5.3.1

Divide each term in $441 P x = 728 - 35 P$ by $441 P$ .

$\frac{441 P x}{441 P} = \frac{728}{441 P} + \frac{- 35 P}{441 P}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $441$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{441 P x}{441 P} = \frac{728}{441 P} + \frac{- 35 P}{441 P}$

Step 5.3.2.1.2

Rewrite the expression.

$\frac{P x}{P} = \frac{728}{441 P} + \frac{- 35 P}{441 P}$

Step 5.3.2.2

Cancel the common factor of $P$ .

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Step 5.3.2.2.1

Cancel the common factor.

$\frac{P x}{P} = \frac{728}{441 P} + \frac{- 35 P}{441 P}$

Step 5.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{728}{441 P} + \frac{- 35 P}{441 P}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Simplify each term.

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Step 5.3.3.1.1

Cancel the common factor of $728$ and $441$ .

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Step 5.3.3.1.1.1

Factor $7$ out of $728$ .

$x = \frac{7 (104)}{441 P} + \frac{- 35 P}{441 P}$

Step 5.3.3.1.1.2

Cancel the common factors.

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Step 5.3.3.1.1.2.1

Factor $7$ out of $441 P$ .

$x = \frac{7 (104)}{7 (63 P)} + \frac{- 35 P}{441 P}$

Step 5.3.3.1.1.2.2

Cancel the common factor.

$x = \frac{7 \cdot 104}{7 (63 P)} + \frac{- 35 P}{441 P}$

Step 5.3.3.1.1.2.3

Rewrite the expression.

$x = \frac{104}{63 P} + \frac{- 35 P}{441 P}$

Step 5.3.3.1.2

Cancel the common factor of $- 35$ and $441$ .

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Step 5.3.3.1.2.1

Factor $7$ out of $- 35 P$ .

$x = \frac{104}{63 P} + \frac{7 (- 5 P)}{441 P}$

Step 5.3.3.1.2.2

Cancel the common factors.

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Step 5.3.3.1.2.2.1

Factor $7$ out of $441 P$ .

$x = \frac{104}{63 P} + \frac{7 (- 5 P)}{7 (63 P)}$

Step 5.3.3.1.2.2.2

Cancel the common factor.

$x = \frac{104}{63 P} + \frac{7 (- 5 P)}{7 (63 P)}$

Step 5.3.3.1.2.2.3

Rewrite the expression.

$x = \frac{104}{63 P} + \frac{- 5 P}{63 P}$

Step 5.3.3.1.3

Cancel the common factor of $P$ .

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Step 5.3.3.1.3.1

Cancel the common factor.

$x = \frac{104}{63 P} + \frac{- 5 P}{63 P}$

Step 5.3.3.1.3.2

Rewrite the expression.

$x = \frac{104}{63 P} + \frac{- 5}{63}$

Step 5.3.3.1.4

Move the negative in front of the fraction.

$x = \frac{104}{63 P} - \frac{5}{63}$

Step 6

To rewrite as a function of $P$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $P$ is on the other side.

$f (P) = \frac{104}{63 P} - \frac{5}{63}$