Pre-Algebra Examples

$\frac{c + 1}{c - 5} \div \frac{c - 2}{c^{2} - 7 c + 10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c + 1}{c - 5} \cdot \frac{c^{2} - 7 c + 10}{c - 2}$

Step 2

Factor $c^{2} - 7 c + 10$ 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 $10$ and whose sum is $- 7$ .

$- 5, - 2$

Step 2.2

Write the factored form using these integers.

$\frac{c + 1}{c - 5} \cdot \frac{(c - 5) (c - 2)}{c - 2}$

Step 3

Cancel the common factor of $c - 5$ .

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Step 3.1

Cancel the common factor.

$\frac{c + 1}{c - 5} \cdot \frac{(c - 5) (c - 2)}{c - 2}$

Step 3.2

Rewrite the expression.

$(c + 1) \frac{c - 2}{c - 2}$

Step 4

Cancel the common factor of $c - 2$ .

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Step 4.1

Cancel the common factor.

$(c + 1) \frac{c - 2}{c - 2}$

Step 4.2

Rewrite the expression.

$(c + 1) \cdot 1$

Step 5

Multiply $c + 1$ by $1$ .

$c + 1$