Basic Math Examples

$\frac{p^{2} + 3 p - 4}{p^{2} + 6 p + 8} \div (p - 1)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{p^{2} + 3 p - 4}{p^{2} + 6 p + 8}}{p - 1}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{p^{2} + 3 p - 4}{p^{2} + 6 p + 8} \cdot \frac{1}{p - 1}$

Step 3

Factor $p^{2} + 3 p - 4$ 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 $- 4$ and whose sum is $3$ .

$- 1, 4$

Step 3.2

Write the factored form using these integers.

$\frac{(p - 1) (p + 4)}{p^{2} + 6 p + 8} \cdot \frac{1}{p - 1}$

Step 4

Factor $p^{2} + 6 p + 8$ 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 $8$ and whose sum is $6$ .

$2, 4$

Step 4.2

Write the factored form using these integers.

$\frac{(p - 1) (p + 4)}{(p + 2) (p + 4)} \cdot \frac{1}{p - 1}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $p - 1$ .

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Step 5.1.1

Cancel the common factor.

$\frac{(p - 1) (p + 4)}{(p + 2) (p + 4)} \cdot \frac{1}{p - 1}$

Step 5.1.2

Rewrite the expression.

$\frac{p + 4}{(p + 2) (p + 4)}$

Step 5.2

Cancel the common factor of $p + 4$ .

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Step 5.2.1

Cancel the common factor.

$\frac{p + 4}{(p + 2) (p + 4)}$

Step 5.2.2

Rewrite the expression.

$\frac{1}{p + 2}$