Algebra Examples

$\frac{5 n^{2} - 5 n}{n^{2} - 5 n - 6}$

Step 1

Factor $5 n$ out of $5 n^{2} - 5 n$ .

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Step 1.1

Factor $5 n$ out of $5 n^{2}$ .

$\frac{5 n (n) - 5 n}{n^{2} - 5 n - 6}$

Step 1.2

Factor $5 n$ out of $- 5 n$ .

$\frac{5 n (n) + 5 n (- 1)}{n^{2} - 5 n - 6}$

Step 1.3

Factor $5 n$ out of $5 n (n) + 5 n (- 1)$ .

$\frac{5 n (n - 1)}{n^{2} - 5 n - 6}$

Step 2

Factor $n^{2} - 5 n - 6$ 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 $- 5$ .

$- 6, 1$

Step 2.2

Write the factored form using these integers.

$\frac{5 n (n - 1)}{(n - 6) (n + 1)}$