Algebra Examples

$\frac{10}{x - 3} - \frac{2 x + 9}{x - 3} + \frac{5 x - 7}{x - 3}$

Step 1

Combine the numerators over the common denominator.

$\frac{10 - (2 x + 9) + 5 x - 7}{x - 3}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{10 - (2 x) - 1 \cdot 9 + 5 x - 7}{x - 3}$

Step 2.2

Multiply $2$ by $- 1$ .

$\frac{10 - 2 x - 1 \cdot 9 + 5 x - 7}{x - 3}$

Step 2.3

Multiply $- 1$ by $9$ .

$\frac{10 - 2 x - 9 + 5 x - 7}{x - 3}$

Step 3

Simplify terms.

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Step 3.1

Subtract $9$ from $10$ .

$\frac{- 2 x + 1 + 5 x - 7}{x - 3}$

Step 3.2

Add $- 2 x$ and $5 x$ .

$\frac{3 x + 1 - 7}{x - 3}$

Step 3.3

Subtract $7$ from $1$ .

$\frac{3 x - 6}{x - 3}$

Step 3.4

Factor $3$ out of $3 x - 6$ .

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Step 3.4.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{x - 3}$

Step 3.4.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{x - 3}$

Step 3.4.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{x - 3}$