Algebra Examples

$s = \frac{3 r}{t - 1}$

Step 1

Rewrite the equation as $\frac{3 r}{t - 1} = s$ .

$\frac{3 r}{t - 1} = s$

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.

$t - 1, 1$

Step 2.2

Remove parentheses.

$t - 1, 1$

Step 2.3

The LCM of one and any expression is the expression.

$t - 1$

Step 3

Multiply each term in $\frac{3 r}{t - 1} = s$ by $t - 1$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{3 r}{t - 1} = s$ by $t - 1$ .

$\frac{3 r}{t - 1} (t - 1) = s (t - 1)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $t - 1$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 r}{t - 1} (t - 1) = s (t - 1)$

Step 3.2.1.2

Rewrite the expression.

$3 r = s (t - 1)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify by multiplying through.

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Step 3.3.1.1

Apply the distributive property.

$3 r = s t + s \cdot - 1$

Step 3.3.1.2

Move $- 1$ to the left of $s$ .

$3 r = s t - 1 \cdot s$

Step 3.3.2

Rewrite $- 1 s$ as $- s$ .

$3 r = s t - s$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $s t - s = 3 r$ .

$s t - s = 3 r$

Step 4.2

Add $s$ to both sides of the equation.

$s t = 3 r + s$

Step 4.3

Divide each term in $s t = 3 r + s$ by $s$ and simplify.

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Step 4.3.1

Divide each term in $s t = 3 r + s$ by $s$ .

$\frac{s t}{s} = \frac{3 r}{s} + \frac{s}{s}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $s$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{s t}{s} = \frac{3 r}{s} + \frac{s}{s}$

Step 4.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{3 r}{s} + \frac{s}{s}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $s$ .

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Step 4.3.3.1.1

Cancel the common factor.

$t = \frac{3 r}{s} + \frac{s}{s}$

Step 4.3.3.1.2

Rewrite the expression.

$t = \frac{3 r}{s} + 1$