Precalculus Examples

$\frac{2 x^{3} - 4 x^{2} - 15 x + 5}{{(x - 1)}^{2}}$

Step 1

Split the fraction $\frac{2 x^{3} - 4 x^{2} - 15 x + 5}{{(x - 1)}^{2}}$ into two fractions.

$\frac{2 x^{3} - 4 x^{2} - 15 x}{{(x - 1)}^{2}} + \frac{5}{{(x - 1)}^{2}}$

Step 2

Split the fraction $\frac{2 x^{3} - 4 x^{2} - 15 x}{{(x - 1)}^{2}}$ into two fractions.

$\frac{2 x^{3} - 4 x^{2}}{{(x - 1)}^{2}} + \frac{- 15 x}{{(x - 1)}^{2}} + \frac{5}{{(x - 1)}^{2}}$

Step 3

Split the fraction $\frac{2 x^{3} - 4 x^{2}}{{(x - 1)}^{2}}$ into two fractions.

$\frac{2 x^{3}}{{(x - 1)}^{2}} + \frac{- 4 x^{2}}{{(x - 1)}^{2}} + \frac{- 15 x}{{(x - 1)}^{2}} + \frac{5}{{(x - 1)}^{2}}$

Step 4

Move the negative in front of the fraction.

$\frac{2 x^{3}}{{(x - 1)}^{2}} - \frac{4 x^{2}}{{(x - 1)}^{2}} + \frac{- 15 x}{{(x - 1)}^{2}} + \frac{5}{{(x - 1)}^{2}}$

Step 5

Move the negative in front of the fraction.

$\frac{2 x^{3}}{{(x - 1)}^{2}} - \frac{4 x^{2}}{{(x - 1)}^{2}} - \frac{15 x}{{(x - 1)}^{2}} + \frac{5}{{(x - 1)}^{2}}$