Algebra Examples

$\frac{x - 1}{x^{2} + 5 x - 6} \div \frac{7 x - 56}{x^{2} - 2 x - 48}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 1}{x^{2} + 5 x - 6} \cdot \frac{x^{2} - 2 x - 48}{7 x - 56}$

Step 2

Factor $x^{2} + 5 x - 6$ using the AC method.

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Step 2.1

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 $- 6$ and whose sum is $5$ .

$- 1, 6$

Step 2.2

Write the factored form using these integers.

$\frac{x - 1}{(x - 1) (x + 6)} \cdot \frac{x^{2} - 2 x - 48}{7 x - 56}$

Step 3

Cancel the common factor of $x - 1$ .

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Step 3.1

Cancel the common factor.

$\frac{x - 1}{(x - 1) (x + 6)} \cdot \frac{x^{2} - 2 x - 48}{7 x - 56}$

Step 3.2

Rewrite the expression.

$\frac{1}{x + 6} \cdot \frac{x^{2} - 2 x - 48}{7 x - 56}$

Step 4

Factor $x^{2} - 2 x - 48$ using the AC method.

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Step 4.1

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 $- 48$ and whose sum is $- 2$ .

$- 8, 6$

Step 4.2

Write the factored form using these integers.

$\frac{1}{x + 6} \cdot \frac{(x - 8) (x + 6)}{7 x - 56}$

Step 5

Factor $7$ out of $7 x - 56$ .

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Step 5.1

Factor $7$ out of $7 x$ .

$\frac{1}{x + 6} \cdot \frac{(x - 8) (x + 6)}{7 (x) - 56}$

Step 5.2

Factor $7$ out of $- 56$ .

$\frac{1}{x + 6} \cdot \frac{(x - 8) (x + 6)}{7 x + 7 \cdot - 8}$

Step 5.3

Factor $7$ out of $7 x + 7 \cdot - 8$ .

$\frac{1}{x + 6} \cdot \frac{(x - 8) (x + 6)}{7 (x - 8)}$

Step 6

Cancel the common factor of $x + 6$ .

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Step 6.1

Factor $x + 6$ out of $(x - 8) (x + 6)$ .

$\frac{1}{x + 6} \cdot \frac{(x + 6) (x - 8)}{7 (x - 8)}$

Step 6.2

Cancel the common factor.

$\frac{1}{x + 6} \cdot \frac{(x + 6) (x - 8)}{7 (x - 8)}$

Step 6.3

Rewrite the expression.

$\frac{x - 8}{7 (x - 8)}$

Step 7

Cancel the common factor of $x - 8$ .

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Step 7.1

Cancel the common factor.

$\frac{x - 8}{7 (x - 8)}$

Step 7.2

Rewrite the expression.

$\frac{1}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$