Algebra Examples

$f = \frac{3 m + 4}{m - 1}$

Step 1

Multiply the equation by $m - 1$ .

$(m - 1) (f) = (\frac{3 m + 4}{m - 1}) (m - 1)$

Step 2

Simplify the left side.

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Step 2.1

Simplify $(m - 1) (f)$ .

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Step 2.1.1

Apply the distributive property.

$m f - 1 f = (\frac{3 m + 4}{m - 1}) (m - 1)$

Step 2.1.2

Rewrite $- 1 f$ as $- f$ .

$m f - f = (\frac{3 m + 4}{m - 1}) (m - 1)$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $m - 1$ .

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Step 3.1.1

Cancel the common factor.

$m f - f = \frac{3 m + 4}{m - 1} (m - 1)$

Step 3.1.2

Rewrite the expression.

$m f - f = 3 m + 4$

Step 4

Solve for $m$ .

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Step 4.1

Subtract $3 m$ from both sides of the equation.

$m f - f - 3 m = 4$

Step 4.2

Add $f$ to both sides of the equation.

$m f - 3 m = 4 + f$

Step 4.3

Factor $m$ out of $m f - 3 m$ .

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Step 4.3.1

Factor $m$ out of $m f$ .

$m (f) - 3 m = 4 + f$

Step 4.3.2

Factor $m$ out of $- 3 m$ .

$m (f) + m \cdot - 3 = 4 + f$

Step 4.3.3

Factor $m$ out of $m (f) + m \cdot - 3$ .

$m (f - 3) = 4 + f$

Step 4.4

Divide each term in $m (f - 3) = 4 + f$ by $f - 3$ and simplify.

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Step 4.4.1

Divide each term in $m (f - 3) = 4 + f$ by $f - 3$ .

$\frac{m (f - 3)}{f - 3} = \frac{4}{f - 3} + \frac{f}{f - 3}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $f - 3$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{m (f - 3)}{f - 3} = \frac{4}{f - 3} + \frac{f}{f - 3}$

Step 4.4.2.1.2

Divide $m$ by $1$ .

$m = \frac{4}{f - 3} + \frac{f}{f - 3}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$m = \frac{4 + f}{f - 3}$