Algebra Examples

$\frac{4 x + 1}{x - 5} - \frac{3 x - 4}{x - 5}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 x + 1 - (3 x - 4)}{x - 5}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{4 x + 1 - (3 x) - - 4}{x - 5}$

Step 2.2

Multiply $3$ by $- 1$ .

$\frac{4 x + 1 - 3 x - - 4}{x - 5}$

Step 2.3

Multiply $- 1$ by $- 4$ .

$\frac{4 x + 1 - 3 x + 4}{x - 5}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $3 x$ from $4 x$ .

$\frac{x + 1 + 4}{x - 5}$

Step 3.2

Add $1$ and $4$ .

$\frac{x + 5}{x - 5}$