Trigonometry Examples

$t = \frac{3 - 2 p}{p}$

Step 1

Rewrite the equation as $\frac{3 - 2 p}{p} = t$ .

$\frac{3 - 2 p}{p} = t$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$p, 1$

Step 2.2

The LCM of one and any expression is the expression.

$p$

Step 3

Multiply each term in $\frac{3 - 2 p}{p} = t$ by $p$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{3 - 2 p}{p} = t$ by $p$ .

$\frac{3 - 2 p}{p} p = t p$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $p$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 - 2 p}{p} p = t p$

Step 3.2.1.2

Rewrite the expression.

$3 - 2 p = t p$

Step 4

Solve the equation.

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Step 4.1

Subtract $t p$ from both sides of the equation.

$3 - 2 p - t p = 0$

Step 4.2

Subtract $3$ from both sides of the equation.

$- 2 p - t p = - 3$

Step 4.3

Factor $p$ out of $- 2 p - t p$ .

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Step 4.3.1

Factor $p$ out of $- 2 p$ .

$p \cdot - 2 - t p = - 3$

Step 4.3.2

Factor $p$ out of $- t p$ .

$p \cdot - 2 + p (- t) = - 3$

Step 4.3.3

Factor $p$ out of $p \cdot - 2 + p (- t)$ .

$p (- 2 - t) = - 3$

Step 4.4

Divide each term in $p (- 2 - t) = - 3$ by $- 2 - t$ and simplify.

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Step 4.4.1

Divide each term in $p (- 2 - t) = - 3$ by $- 2 - t$ .

$\frac{p (- 2 - t)}{- 2 - t} = \frac{- 3}{- 2 - t}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $- 2 - t$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{p (- 2 - t)}{- 2 - t} = \frac{- 3}{- 2 - t}$

Step 4.4.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 3}{- 2 - t}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

$p = - \frac{3}{- 2 - t}$

Step 4.4.3.2

Rewrite $- 2$ as $- 1 (2)$ .

$p = - \frac{3}{- 1 (2) - t}$

Step 4.4.3.3

Factor $- 1$ out of $- t$ .

$p = - \frac{3}{- 1 (2) - (t)}$

Step 4.4.3.4

Factor $- 1$ out of $- 1 (2) - (t)$ .

$p = - \frac{3}{- 1 (2 + t)}$

Step 4.4.3.5

Simplify the expression.

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Step 4.4.3.5.1

Move the negative in front of the fraction.

$p = - - \frac{3}{2 + t}$

Step 4.4.3.5.2

Multiply $- 1$ by $- 1$ .

$p = 1 \frac{3}{2 + t}$

Step 4.4.3.5.3

Multiply $\frac{3}{2 + t}$ by $1$ .

$p = \frac{3}{2 + t}$