Finite Math Examples

$\frac{x^{2} + 2 x - 35}{x^{2} \cdot (4 x) - 21}$

Step 1

Factor $x^{2} + 2 x - 35$ 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 $- 35$ and whose sum is $2$ .

$- 5, 7$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 5) (x + 7)}{x^{2} \cdot (4 x) - 21}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{(x - 5) (x + 7)}{4 x^{2} x - 21}$

Step 2.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.2.1

Move $x$ .

$\frac{(x - 5) (x + 7)}{4 (x \cdot x^{2}) - 21}$

Step 2.2.2

Multiply $x$ by $x^{2}$ .

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Step 2.2.2.1

Raise $x$ to the power of $1$ .

$\frac{(x - 5) (x + 7)}{4 (x^{1} x^{2}) - 21}$

Step 2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(x - 5) (x + 7)}{4 x^{1 + 2} - 21}$

Step 2.2.3

Add $1$ and $2$ .

$\frac{(x - 5) (x + 7)}{4 x^{3} - 21}$