Algebra Examples

$\frac{7}{x} - \frac{5 x + 7}{x - 9}$

Step 1

To write $\frac{7}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 9}{x - 9}$ .

$\frac{7}{x} \cdot \frac{x - 9}{x - 9} - \frac{5 x + 7}{x - 9}$

Step 2

To write $- \frac{5 x + 7}{x - 9}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{7}{x} \cdot \frac{x - 9}{x - 9} - \frac{5 x + 7}{x - 9} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x (x - 9)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{7}{x}$ by $\frac{x - 9}{x - 9}$ .

$\frac{7 (x - 9)}{x (x - 9)} - \frac{5 x + 7}{x - 9} \cdot \frac{x}{x}$

Step 3.2

Multiply $\frac{5 x + 7}{x - 9}$ by $\frac{x}{x}$ .

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

Step 3.3

Reorder the factors of $(x - 9) x$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{7 x + 7 \cdot - 9 - (5 x + 7) x}{x (x - 9)}$

Step 5.2

Multiply $7$ by $- 9$ .

$\frac{7 x - 63 - (5 x + 7) x}{x (x - 9)}$

Step 5.3

Apply the distributive property.

$\frac{7 x - 63 + (- (5 x) - 1 \cdot 7) x}{x (x - 9)}$

Step 5.4

Multiply $5$ by $- 1$ .

$\frac{7 x - 63 + (- 5 x - 1 \cdot 7) x}{x (x - 9)}$

Step 5.5

Multiply $- 1$ by $7$ .

$\frac{7 x - 63 + (- 5 x - 7) x}{x (x - 9)}$

Step 5.6

Apply the distributive property.

$\frac{7 x - 63 - 5 x \cdot x - 7 x}{x (x - 9)}$

Step 5.7

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

Tap for more steps...

Step 5.7.1

Move $x$ .

$\frac{7 x - 63 - 5 (x \cdot x) - 7 x}{x (x - 9)}$

Step 5.7.2

Multiply $x$ by $x$ .

$\frac{7 x - 63 - 5 x^{2} - 7 x}{x (x - 9)}$

Step 5.8

Subtract $7 x$ from $7 x$ .

$\frac{- 63 - 5 x^{2} + 0}{x (x - 9)}$

Step 5.9

Add $- 63 - 5 x^{2}$ and $0$ .

$\frac{- 63 - 5 x^{2}}{x (x - 9)}$

Step 6

Simplify with factoring out.

Tap for more steps...

Step 6.1

Rewrite $- 63$ as $- 1 (63)$ .

$\frac{- 1 (63) - 5 x^{2}}{x (x - 9)}$

Step 6.2

Factor $- 1$ out of $- 5 x^{2}$ .

$\frac{- 1 (63) - (5 x^{2})}{x (x - 9)}$

Step 6.3

Factor $- 1$ out of $- 1 (63) - (5 x^{2})$ .

$\frac{- 1 (63 + 5 x^{2})}{x (x - 9)}$

Step 6.4

Move the negative in front of the fraction.

$- \frac{63 + 5 x^{2}}{x (x - 9)}$