Basic Math Examples

$\frac{d + 3}{d^{2}} \cdot \frac{3 d}{d^{2} + 7 d + 12}$

Step 1

Factor $d^{2} + 7 d + 12$ using the AC method.

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Step 1.1

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 $12$ and whose sum is $7$ .

$3, 4$

Step 1.2

Write the factored form using these integers.

$\frac{d + 3}{d^{2}} \cdot \frac{3 d}{(d + 3) (d + 4)}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $d + 3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{d + 3}{d^{2}} \cdot \frac{3 d}{(d + 3) (d + 4)}$

Step 2.1.2

Rewrite the expression.

$\frac{1}{d^{2}} \cdot \frac{3 d}{d + 4}$

Step 2.2

Cancel the common factor of $d$ .

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Step 2.2.1

Factor $d$ out of $d^{2}$ .

$\frac{1}{d \cdot d} \cdot \frac{3 d}{d + 4}$

Step 2.2.2

Factor $d$ out of $3 d$ .

$\frac{1}{d \cdot d} \cdot \frac{d \cdot 3}{d + 4}$

Step 2.2.3

Cancel the common factor.

$\frac{1}{d \cdot d} \cdot \frac{d \cdot 3}{d + 4}$

Step 2.2.4

Rewrite the expression.

$\frac{1}{d} \cdot \frac{3}{d + 4}$

Step 2.3

Multiply $\frac{1}{d}$ by $\frac{3}{d + 4}$ .

$\frac{3}{d (d + 4)}$