Finite Math Examples

$\frac{x - 3}{x + 1} - \frac{4}{x^{2} + x}$

Step 1

Factor $x$ out of $x^{2} + x$ .

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Step 1.1

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

$\frac{x - 3}{x + 1} - \frac{4}{x \cdot x + x}$

Step 1.2

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

$\frac{x - 3}{x + 1} - \frac{4}{x \cdot x + x^{1}}$

Step 1.3

Factor $x$ out of $x^{1}$ .

$\frac{x - 3}{x + 1} - \frac{4}{x \cdot x + x \cdot 1}$

Step 1.4

Factor $x$ out of $x \cdot x + x \cdot 1$ .

$\frac{x - 3}{x + 1} - \frac{4}{x (x + 1)}$

Step 2

To write $\frac{x - 3}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{x - 3}{x + 1} \cdot \frac{x}{x} - \frac{4}{x (x + 1)}$

Step 3

Write each expression with a common denominator of $(x + 1) x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x - 3}{x + 1}$ by $\frac{x}{x}$ .

$\frac{(x - 3) x}{(x + 1) x} - \frac{4}{x (x + 1)}$

Step 3.2

Reorder the factors of $(x + 1) x$ .

$\frac{(x - 3) x}{x (x + 1)} - \frac{4}{x (x + 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{(x - 3) x - 4}{x (x + 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{x \cdot x - 3 x - 4}{x (x + 1)}$

Step 5.2

Multiply $x$ by $x$ .

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

Step 5.3

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

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Step 5.3.1

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 $- 3$ .

$- 4, 1$

Step 5.3.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 1)}{x (x + 1)}$

Step 6

Cancel the common factor of $x + 1$ .

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Step 6.1

Cancel the common factor.

$\frac{(x - 4) (x + 1)}{x (x + 1)}$

Step 6.2

Rewrite the expression.

$\frac{x - 4}{x}$