Simplify (x^4+x^3-2x^2)/(x^4-x^3)

$\frac{x^{4} + x^{3} - 2 x^{2}}{x^{4} - x^{3}}$

Step 1

Simplify the numerator.

Factor $x^{2}$ out of $x^{4} + x^{3} - 2 x^{2}$ .

Factor $x^{2}$ out of $x^{4}$ .

$\frac{x^{2} x^{2} + x^{3} - 2 x^{2}}{x^{4} - x^{3}}$

Factor $x^{2}$ out of $x^{3}$ .

$\frac{x^{2} x^{2} + x^{2} x - 2 x^{2}}{x^{4} - x^{3}}$

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

$\frac{x^{2} x^{2} + x^{2} x + x^{2} \cdot - 2}{x^{4} - x^{3}}$

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

$\frac{x^{2} (x^{2} + x) + x^{2} \cdot - 2}{x^{4} - x^{3}}$

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

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

Factor $x^{2} + x - 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Write the factored form using these integers.

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

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

Step 2

Simplify terms.

Factor $x^{3}$ out of $x^{4} - x^{3}$ .

Factor $x^{3}$ out of $x^{4}$ .

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

Factor $x^{3}$ out of $- x^{3}$ .

$\frac{x^{2} (x - 1) (x + 2)}{x^{3} x + x^{3} \cdot - 1}$

Factor $x^{3}$ out of $x^{3} x + x^{3} \cdot - 1$ .

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

Cancel the common factor of $x^{2}$ and $x^{3}$ .

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

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

Cancel the common factors.

Factor $x^{2}$ out of $x^{3} (x - 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 2}{x}$

Simplify (x^4+x^3-2x^2)/(x^4-x^3)

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