Basic Math Examples

$\frac{c^{2} + 3 c + 2}{c^{2} - 4 c + 3} \div \frac{c + 2}{c - 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2} + 3 c + 2}{c^{2} - 4 c + 3} \cdot \frac{c - 3}{c + 2}$

Step 2

Factor $c^{2} + 3 c + 2$ 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 $2$ and whose sum is $3$ .

$1, 2$

Step 2.2

Write the factored form using these integers.

$\frac{(c + 1) (c + 2)}{c^{2} - 4 c + 3} \cdot \frac{c - 3}{c + 2}$

Step 3

Factor $c^{2} - 4 c + 3$ using the AC method.

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Step 3.1

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 $3$ and whose sum is $- 4$ .

$- 3, - 1$

Step 3.2

Write the factored form using these integers.

$\frac{(c + 1) (c + 2)}{(c - 3) (c - 1)} \cdot \frac{c - 3}{c + 2}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $c + 2$ .

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Step 4.1.1

Factor $c + 2$ out of $(c + 1) (c + 2)$ .

$\frac{(c + 2) (c + 1)}{(c - 3) (c - 1)} \cdot \frac{c - 3}{c + 2}$

Step 4.1.2

Cancel the common factor.

$\frac{(c + 2) (c + 1)}{(c - 3) (c - 1)} \cdot \frac{c - 3}{c + 2}$

Step 4.1.3

Rewrite the expression.

$\frac{c + 1}{(c - 3) (c - 1)} (c - 3)$

Step 4.2

Cancel the common factor of $c - 3$ .

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Step 4.2.1

Cancel the common factor.

$\frac{c + 1}{(c - 3) (c - 1)} (c - 3)$

Step 4.2.2

Rewrite the expression.

$\frac{c + 1}{c - 1}$