Pre-Algebra Examples

$\frac{m}{m - 4} - 5 = \frac{4}{m - 4}$

Step 1

Simplify $\frac{m}{m - 4} - 5$ .

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Step 1.1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{m - 4}{m - 4}$ .

$\frac{m}{m - 4} - 5 \cdot \frac{m - 4}{m - 4} = \frac{4}{m - 4}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $- 5$ and $\frac{m - 4}{m - 4}$ .

$\frac{m}{m - 4} + \frac{- 5 (m - 4)}{m - 4} = \frac{4}{m - 4}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{m - 5 (m - 4)}{m - 4} = \frac{4}{m - 4}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Apply the distributive property.

$\frac{m - 5 m - 5 \cdot - 4}{m - 4} = \frac{4}{m - 4}$

Step 1.3.2

Multiply $- 5$ by $- 4$ .

$\frac{m - 5 m + 20}{m - 4} = \frac{4}{m - 4}$

Step 1.3.3

Subtract $5 m$ from $m$ .

$\frac{- 4 m + 20}{m - 4} = \frac{4}{m - 4}$

Step 1.3.4

Factor $4$ out of $- 4 m + 20$ .

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Step 1.3.4.1

Factor $4$ out of $- 4 m$ .

$\frac{4 (- m) + 20}{m - 4} = \frac{4}{m - 4}$

Step 1.3.4.2

Factor $4$ out of $20$ .

$\frac{4 (- m) + 4 (5)}{m - 4} = \frac{4}{m - 4}$

Step 1.3.4.3

Factor $4$ out of $4 (- m) + 4 (5)$ .

$\frac{4 (- m + 5)}{m - 4} = \frac{4}{m - 4}$

Step 1.4

Simplify with factoring out.

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Step 1.4.1

Factor $- 1$ out of $- m$ .

$\frac{4 (- (m) + 5)}{m - 4} = \frac{4}{m - 4}$

Step 1.4.2

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{4 (- (m) - 1 (- 5))}{m - 4} = \frac{4}{m - 4}$

Step 1.4.3

Factor $- 1$ out of $- (m) - 1 (- 5)$ .

$\frac{4 (- (m - 5))}{m - 4} = \frac{4}{m - 4}$

Step 1.4.4

Simplify the expression.

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Step 1.4.4.1

Rewrite $- (m - 5)$ as $- 1 (m - 5)$ .

$\frac{4 (- 1 (m - 5))}{m - 4} = \frac{4}{m - 4}$

Step 1.4.4.2

Move the negative in front of the fraction.

$- \frac{4 (m - 5)}{m - 4} = \frac{4}{m - 4}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 3