Algebra Examples

$\frac{9 x}{2 (x + 1)} - \frac{x}{x + 1}$

Step 1

To write $- \frac{x}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 x}{2 (x + 1)} - \frac{x}{x + 1} \cdot \frac{2}{2}$

Step 2

Write each expression with a common denominator of $2 (x + 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{x}{x + 1}$ by $\frac{2}{2}$ .

$\frac{9 x}{2 (x + 1)} - \frac{x \cdot 2}{(x + 1) \cdot 2}$

Step 2.2

Reorder the factors of $(x + 1) \cdot 2$ .

$\frac{9 x}{2 (x + 1)} - \frac{x \cdot 2}{2 (x + 1)}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 x - x \cdot 2}{2 (x + 1)}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $9 x - x \cdot 2$ .

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Step 4.1.1

Factor $x$ out of $9 x$ .

$\frac{x \cdot 9 - x \cdot 2}{2 (x + 1)}$

Step 4.1.2

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

$\frac{x \cdot 9 + x (- 1 \cdot 2)}{2 (x + 1)}$

Step 4.1.3

Factor $x$ out of $x \cdot 9 + x (- 1 \cdot 2)$ .

$\frac{x (9 - 1 \cdot 2)}{2 (x + 1)}$

Step 4.2

Multiply $- 1$ by $2$ .

$\frac{x (9 - 2)}{2 (x + 1)}$

Step 4.3

Subtract $2$ from $9$ .

$\frac{x \cdot 7}{2 (x + 1)}$

Step 5

Move $7$ to the left of $x$ .

$\frac{7 x}{2 (x + 1)}$