Algebra Examples

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

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Write $5 x$ as a fraction with denominator $1$ .

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

Step 1.2

Multiply $\frac{5 x}{1}$ by $\frac{x - 5}{x - 5}$ .

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

Step 1.3

Multiply $\frac{5 x}{1}$ by $\frac{x - 5}{x - 5}$ .

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

Step 1.4

Write $7$ as a fraction with denominator $1$ .

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

Step 1.5

Multiply $\frac{7}{1}$ by $\frac{x - 5}{x - 5}$ .

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

Step 1.6

Multiply $\frac{7}{1}$ by $\frac{x - 5}{x - 5}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Apply the distributive property.

$\frac{5 x \cdot x + 5 x \cdot - 5 + 7 (x - 5) - 2 x}{x - 5}$

Step 3.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 3.2.1

Move $x$ .

$\frac{5 (x \cdot x) + 5 x \cdot - 5 + 7 (x - 5) - 2 x}{x - 5}$

Step 3.2.2

Multiply $x$ by $x$ .

$\frac{5 x^{2} + 5 x \cdot - 5 + 7 (x - 5) - 2 x}{x - 5}$

Step 3.3

Multiply $- 5$ by $5$ .

$\frac{5 x^{2} - 25 x + 7 (x - 5) - 2 x}{x - 5}$

Step 3.4

Apply the distributive property.

$\frac{5 x^{2} - 25 x + 7 x + 7 \cdot - 5 - 2 x}{x - 5}$

Step 3.5

Multiply $7$ by $- 5$ .

$\frac{5 x^{2} - 25 x + 7 x - 35 - 2 x}{x - 5}$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Add $- 25 x$ and $7 x$ .

$\frac{5 x^{2} - 18 x - 35 - 2 x}{x - 5}$

Step 4.2

Subtract $2 x$ from $- 18 x$ .

$\frac{5 x^{2} - 20 x - 35}{x - 5}$

Step 4.3

Factor $5$ out of $5 x^{2} - 20 x - 35$ .

Tap for more steps...

Step 4.3.1

Factor $5$ out of $5 x^{2}$ .

$\frac{5 (x^{2}) - 20 x - 35}{x - 5}$

Step 4.3.2

Factor $5$ out of $- 20 x$ .

$\frac{5 (x^{2}) + 5 (- 4 x) - 35}{x - 5}$

Step 4.3.3

Factor $5$ out of $- 35$ .

$\frac{5 x^{2} + 5 (- 4 x) + 5 \cdot - 7}{x - 5}$

Step 4.3.4

Factor $5$ out of $5 x^{2} + 5 (- 4 x)$ .

$\frac{5 (x^{2} - 4 x) + 5 \cdot - 7}{x - 5}$

Step 4.3.5

Factor $5$ out of $5 (x^{2} - 4 x) + 5 \cdot - 7$ .

$\frac{5 (x^{2} - 4 x - 7)}{x - 5}$