Precalculus Examples

$\frac{(2 x^{2} - 5 x + 8) - (2 a^{2} - 5 a + 8)}{x - a}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the distributive property.

$\frac{2 x^{2} - 5 x + 8 - (2 a^{2}) - (- 5 a) - 1 \cdot 8}{x - a}$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$\frac{2 x^{2} - 5 x + 8 - 2 a^{2} - (- 5 a) - 1 \cdot 8}{x - a}$

Step 1.2.2

Multiply $- 5$ by $- 1$ .

$\frac{2 x^{2} - 5 x + 8 - 2 a^{2} + 5 a - 1 \cdot 8}{x - a}$

Step 1.2.3

Multiply $- 1$ by $8$ .

$\frac{2 x^{2} - 5 x + 8 - 2 a^{2} + 5 a - 8}{x - a}$

Step 1.3

Subtract $8$ from $8$ .

$\frac{2 x^{2} - 5 x - 2 a^{2} + 5 a + 0}{x - a}$

Step 1.4

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

$\frac{2 x^{2} - 5 x - 2 a^{2} + 5 a}{x - a}$

Step 2

Split the fraction $\frac{2 x^{2} - 5 x - 2 a^{2} + 5 a}{x - a}$ into two fractions.

$\frac{2 x^{2} - 5 x - 2 a^{2}}{x - a} + \frac{5 a}{x - a}$

Step 3

Split the fraction $\frac{2 x^{2} - 5 x - 2 a^{2}}{x - a}$ into two fractions.

$\frac{2 x^{2} - 5 x}{x - a} + \frac{- 2 a^{2}}{x - a} + \frac{5 a}{x - a}$

Step 4

Split the fraction $\frac{2 x^{2} - 5 x}{x - a}$ into two fractions.

$\frac{2 x^{2}}{x - a} + \frac{- 5 x}{x - a} + \frac{- 2 a^{2}}{x - a} + \frac{5 a}{x - a}$

Step 5

Move the negative in front of the fraction.

$\frac{2 x^{2}}{x - a} - \frac{5 x}{x - a} + \frac{- 2 a^{2}}{x - a} + \frac{5 a}{x - a}$

Step 6

Move the negative in front of the fraction.

$\frac{2 x^{2}}{x - a} - \frac{5 x}{x - a} - \frac{2 a^{2}}{x - a} + \frac{5 a}{x - a}$