Simplify (x^2-9)/(x^2+5x+6)-(3x-14)/(4x+8)

$\frac{x^{2} - 9}{x^{2} + 5 x + 6} - \frac{3 x - 14}{4 x + 8}$

Simplify each term.

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{x^{2} - 3^{2}}{x^{2} + 5 x + 6} - \frac{3 x - 14}{4 x + 8}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{(x + 3) (x - 3)}{x^{2} + 5 x + 6} - \frac{3 x - 14}{4 x + 8}$

Factor $x^{2} + 5 x + 6$ using the AC method.

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 $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

$\frac{(x + 3) (x - 3)}{(x + 2) (x + 3)} - \frac{3 x - 14}{4 x + 8}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x + 3) (x - 3)}{(x + 2) (x + 3)} - \frac{3 x - 14}{4 x + 8}$

Rewrite the expression.

$\frac{x - 3}{x + 2} - \frac{3 x - 14}{4 x + 8}$

Factor $4$ out of $4 x + 8$ .

Factor $4$ out of $4 x$ .

$\frac{x - 3}{x + 2} - \frac{3 x - 14}{4 (x) + 8}$

Factor $4$ out of $8$ .

$\frac{x - 3}{x + 2} - \frac{3 x - 14}{4 x + 4 \cdot 2}$

Factor $4$ out of $4 x + 4 \cdot 2$ .

$\frac{x - 3}{x + 2} - \frac{3 x - 14}{4 (x + 2)}$

To write $\frac{x - 3}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x - 3}{x + 2} \cdot \frac{4}{4} - \frac{3 x - 14}{4 (x + 2)}$

Write each expression with a common denominator of $(x + 2) \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 3}{x + 2}$ by $\frac{4}{4}$ .

$\frac{(x - 3) \cdot 4}{(x + 2) \cdot 4} - \frac{3 x - 14}{4 (x + 2)}$

Reorder the factors of $(x + 2) \cdot 4$ .

$\frac{(x - 3) \cdot 4}{4 (x + 2)} - \frac{3 x - 14}{4 (x + 2)}$

Combine the numerators over the common denominator.

$\frac{(x - 3) \cdot 4 - (3 x - 14)}{4 (x + 2)}$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 4 - 3 \cdot 4 - (3 x - 14)}{4 (x + 2)}$

Move $4$ to the left of $x$ .

$\frac{4 \cdot x - 3 \cdot 4 - (3 x - 14)}{4 (x + 2)}$

Multiply $- 3$ by $4$ .

$\frac{4 \cdot x - 12 - (3 x - 14)}{4 (x + 2)}$

Apply the distributive property.

$\frac{4 x - 12 - (3 x) - - 14}{4 (x + 2)}$

Multiply $3$ by $- 1$ .

$\frac{4 x - 12 - 3 x - - 14}{4 (x + 2)}$

Multiply $- 1$ by $- 14$ .

$\frac{4 x - 12 - 3 x + 14}{4 (x + 2)}$

Subtract $3 x$ from $4 x$ .

$\frac{x - 12 + 14}{4 (x + 2)}$

Add $- 12$ and $14$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$

Simplify (x^2-9)/(x^2+5x+6)-(3x-14)/(4x+8)

Related Questions

Support LCMGCF.com by disabling your adblocker.