Algebra Examples

$\frac{35 x^{4} - 21 x^{6} - 42 x^{2}}{7 x^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $7 x^{2}$ out of $35 x^{4} - 21 x^{6} - 42 x^{2}$ .

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Step 1.1.1

Factor $7 x^{2}$ out of $35 x^{4}$ .

$\frac{7 x^{2} (5 x^{2}) - 21 x^{6} - 42 x^{2}}{7 x^{2}}$

Step 1.1.2

Factor $7 x^{2}$ out of $- 21 x^{6}$ .

$\frac{7 x^{2} (5 x^{2}) + 7 x^{2} (- 3 x^{4}) - 42 x^{2}}{7 x^{2}}$

Step 1.1.3

Factor $7 x^{2}$ out of $- 42 x^{2}$ .

$\frac{7 x^{2} (5 x^{2}) + 7 x^{2} (- 3 x^{4}) + 7 x^{2} (- 6)}{7 x^{2}}$

Step 1.1.4

Factor $7 x^{2}$ out of $7 x^{2} (5 x^{2}) + 7 x^{2} (- 3 x^{4})$ .

$\frac{7 x^{2} (5 x^{2} - 3 x^{4}) + 7 x^{2} (- 6)}{7 x^{2}}$

Step 1.1.5

Factor $7 x^{2}$ out of $7 x^{2} (5 x^{2} - 3 x^{4}) + 7 x^{2} (- 6)$ .

$\frac{7 x^{2} (5 x^{2} - 3 x^{4} - 6)}{7 x^{2}}$

Step 1.2

Reorder terms.

$\frac{7 x^{2} (- 3 x^{4} + 5 x^{2} - 6)}{7 x^{2}}$

Step 2

Cancel the common factor of $7$ .

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Step 2.1

Cancel the common factor.

$\frac{7 x^{2} (- 3 x^{4} + 5 x^{2} - 6)}{7 x^{2}}$

Step 2.2

Rewrite the expression.

$\frac{x^{2} (- 3 x^{4} + 5 x^{2} - 6)}{x^{2}}$

Step 3

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

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Step 3.1

Cancel the common factor.

$\frac{x^{2} (- 3 x^{4} + 5 x^{2} - 6)}{x^{2}}$

Step 3.2

Divide $- 3 x^{4} + 5 x^{2} - 6$ by $1$ .

$- 3 x^{4} + 5 x^{2} - 6$