Algebra Examples

$\frac{\frac{1}{x} - f (a)}{x - a}$

Step 1

Multiply the numerator and denominator of the fraction by $x$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{1}{x} - f a}{x - a}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{\frac{1}{x} - f a}{x - a}$

Step 1.2

Combine.

$\frac{x (\frac{1}{x} - f a)}{x (x - a)}$

Step 2

Apply the distributive property.

$\frac{x \frac{1}{x} + x (- f a)}{x \cdot x + x (- a)}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\frac{x \frac{1}{x} + x (- f a)}{x \cdot x + x (- a)}$

Step 3.1.2

Rewrite the expression.

$\frac{1 + x (- f a)}{x \cdot x + x (- a)}$

Step 3.2

Rewrite using the commutative property of multiplication.

$\frac{1 - x f a}{x \cdot x + x (- a)}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $x$ by $x$ .

$\frac{1 - x f a}{x^{2} + x (- a)}$

Step 4.2

Rewrite using the commutative property of multiplication.

$\frac{1 - x f a}{x^{2} - x a}$

Step 4.3

Factor $x$ out of $x^{2} - x a$ .

Tap for more steps...

Step 4.3.1

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

$\frac{1 - x f a}{x \cdot x - x a}$

Step 4.3.2

Factor $x$ out of $- x a$ .

$\frac{1 - x f a}{x \cdot x + x (- a)}$

Step 4.3.3

Factor $x$ out of $x \cdot x + x (- a)$ .

$\frac{1 - x f a}{x (x - a)}$