Algebra Examples

$\frac{\frac{x - 5}{x^{2}}}{\frac{2 x - 10}{3 x^{4}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x - 5}{x^{2}} \cdot \frac{3 x^{4}}{2 x - 10}$

Step 2

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

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Step 2.1

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

$\frac{x - 5}{x^{2}} \cdot \frac{x^{2} (3 x^{2})}{2 x - 10}$

Step 2.2

Cancel the common factor.

$\frac{x - 5}{x^{2}} \cdot \frac{x^{2} (3 x^{2})}{2 x - 10}$

Step 2.3

Rewrite the expression.

$(x - 5) \frac{3 x^{2}}{2 x - 10}$

Step 3

Factor $2$ out of $2 x - 10$ .

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Step 3.1

Factor $2$ out of $2 x$ .

$(x - 5) \frac{3 x^{2}}{2 (x) - 10}$

Step 3.2

Factor $2$ out of $- 10$ .

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

Step 3.3

Factor $2$ out of $2 x + 2 \cdot - 5$ .

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

Step 4

Cancel the common factor of $x - 5$ .

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Step 4.1

Factor $x - 5$ out of $2 (x - 5)$ .

$(x - 5) \frac{3 x^{2}}{(x - 5) \cdot 2}$

Step 4.2

Cancel the common factor.

$(x - 5) \frac{3 x^{2}}{(x - 5) \cdot 2}$

Step 4.3

Rewrite the expression.

$\frac{3 x^{2}}{2}$