Pre-Algebra Examples

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{6 x - 60}{42}}$

Step 1

Cancel the common factor of $6 x - 60$ and $42$ .

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Step 1.1

Factor $6$ out of $6 x$ .

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{6 (x) - 60}{42}}$

Step 1.2

Factor $6$ out of $- 60$ .

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{6 x + 6 \cdot - 10}{42}}$

Step 1.3

Factor $6$ out of $6 x + 6 \cdot - 10$ .

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{6 (x - 10)}{42}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $6$ out of $42$ .

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{6 (x - 10)}{6 (7)}}$

Step 1.4.2

Cancel the common factor.

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{6 (x - 10)}{6 \cdot 7}}$

Step 1.4.3

Rewrite the expression.

$\frac{\frac{x^{2} - 20 x + 100}{7 x - 70}}{\frac{x - 10}{7}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 20 x + 100}{7 x - 70} \cdot \frac{7}{x - 10}$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $100$ as $10^{2}$ .

$\frac{x^{2} - 20 x + 10^{2}}{7 x - 70} \cdot \frac{7}{x - 10}$

Step 3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 x = 2 \cdot x \cdot 10$

Step 3.3

Rewrite the polynomial.

$\frac{x^{2} - 2 \cdot x \cdot 10 + 10^{2}}{7 x - 70} \cdot \frac{7}{x - 10}$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 10$ .

$\frac{{(x - 10)}^{2}}{7 x - 70} \cdot \frac{7}{x - 10}$

Step 4

Factor $7$ out of $7 x - 70$ .

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Step 4.1

Factor $7$ out of $7 x$ .

$\frac{{(x - 10)}^{2}}{7 (x) - 70} \cdot \frac{7}{x - 10}$

Step 4.2

Factor $7$ out of $- 70$ .

$\frac{{(x - 10)}^{2}}{7 x + 7 \cdot - 10} \cdot \frac{7}{x - 10}$

Step 4.3

Factor $7$ out of $7 x + 7 \cdot - 10$ .

$\frac{{(x - 10)}^{2}}{7 (x - 10)} \cdot \frac{7}{x - 10}$

Step 5

Cancel the common factor of $x - 10$ .

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Step 5.1

Factor $x - 10$ out of ${(x - 10)}^{2}$ .

$\frac{(x - 10) (x - 10)}{7 (x - 10)} \cdot \frac{7}{x - 10}$

Step 5.2

Cancel the common factor.

$\frac{(x - 10) (x - 10)}{7 (x - 10)} \cdot \frac{7}{x - 10}$

Step 5.3

Rewrite the expression.

$\frac{x - 10}{7 (x - 10)} \cdot 7$

Step 6

Cancel the common factor of $7$ .

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Step 6.1

Cancel the common factor.

$\frac{x - 10}{7 (x - 10)} \cdot 7$

Step 6.2

Rewrite the expression.

$\frac{x - 10}{x - 10}$

Step 7

Cancel the common factor of $x - 10$ .

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Step 7.1

Cancel the common factor.

$\frac{x - 10}{x - 10}$

Step 7.2

Rewrite the expression.

$1$