Pre-Algebra Examples

$\frac{x^{2} - 14 x + 49}{9 x - 63} \div \frac{10 x - 70}{90}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 14 x + 49}{9 x - 63} \cdot \frac{90}{10 x - 70}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{x^{2} - 14 x + 7^{2}}{9 x - 63} \cdot \frac{90}{10 x - 70}$

Step 2.2

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

$14 x = 2 \cdot x \cdot 7$

Step 2.3

Rewrite the polynomial.

$\frac{x^{2} - 2 \cdot x \cdot 7 + 7^{2}}{9 x - 63} \cdot \frac{90}{10 x - 70}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

$\frac{{(x - 7)}^{2}}{9 x - 63} \cdot \frac{90}{10 x - 70}$

Step 3

Factor $9$ out of $9 x - 63$ .

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Step 3.1

Factor $9$ out of $9 x$ .

$\frac{{(x - 7)}^{2}}{9 (x) - 63} \cdot \frac{90}{10 x - 70}$

Step 3.2

Factor $9$ out of $- 63$ .

$\frac{{(x - 7)}^{2}}{9 x + 9 \cdot - 7} \cdot \frac{90}{10 x - 70}$

Step 3.3

Factor $9$ out of $9 x + 9 \cdot - 7$ .

$\frac{{(x - 7)}^{2}}{9 (x - 7)} \cdot \frac{90}{10 x - 70}$

Step 4

Cancel the common factor of $9$ .

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Step 4.1

Factor $9$ out of $90$ .

$\frac{{(x - 7)}^{2}}{9 (x - 7)} \cdot \frac{9 (10)}{10 x - 70}$

Step 4.2

Cancel the common factor.

$\frac{{(x - 7)}^{2}}{9 (x - 7)} \cdot \frac{9 \cdot 10}{10 x - 70}$

Step 4.3

Rewrite the expression.

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

Step 5

Multiply $\frac{{(x - 7)}^{2}}{x - 7}$ by $\frac{10}{10 x - 70}$ .

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

Step 6

Cancel the common factor of ${(x - 7)}^{2}$ and $x - 7$ .

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Step 6.1

Factor $x - 7$ out of ${(x - 7)}^{2} \cdot 10$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Rewrite the expression.

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

Step 7

Cancel the common factor of $10$ and $10 x - 70$ .

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Step 7.1

Factor $10$ out of $(x - 7) \cdot 10$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $10$ out of $10 x$ .

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

Step 7.2.2

Factor $10$ out of $- 70$ .

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

Step 7.2.3

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

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

Step 7.2.4

Cancel the common factor.

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

Step 7.2.5

Rewrite the expression.

$\frac{x - 7}{x - 7}$

Step 8

Cancel the common factor of $x - 7$ .

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Step 8.1

Cancel the common factor.

$\frac{x - 7}{x - 7}$

Step 8.2

Rewrite the expression.

$1$