Simplify 5/(4x^2-36)+4/(2x+6)

$\frac{5}{4 x^{2} - 36} + \frac{4}{2 x + 6}$

Simplify each term.

Simplify the denominator.

Factor $4$ out of $4 x^{2} - 36$ .

Factor $4$ out of $4 x^{2}$ .

$\frac{5}{4 (x^{2}) - 36} + \frac{4}{2 x + 6}$

Factor $4$ out of $- 36$ .

$\frac{5}{4 x^{2} + 4 \cdot - 9} + \frac{4}{2 x + 6}$

Factor $4$ out of $4 x^{2} + 4 \cdot - 9$ .

$\frac{5}{4 (x^{2} - 9)} + \frac{4}{2 x + 6}$

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

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

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 $b = 3$ .

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

Cancel the common factor of $4$ and $2 x + 6$ .

Factor $2$ out of $4$ .

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 \cdot 2}{2 x + 6}$

Cancel the common factors.

Factor $2$ out of $2 x$ .

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 \cdot 2}{2 (x) + 6}$

Factor $2$ out of $6$ .

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 \cdot 2}{2 (x) + 2 (3)}$

Factor $2$ out of $2 (x) + 2 (3)$ .

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 \cdot 2}{2 (x + 3)}$

Cancel the common factor.

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 \cdot 2}{2 (x + 3)}$

Rewrite the expression.

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2}{x + 3}$

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

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2}{x + 3} \cdot \frac{4 (x - 3)}{4 (x - 3)}$

Write each expression with a common denominator of $4 (x + 3) (x - 3)$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 (4 (x - 3))}{(x + 3) (4 (x - 3))}$

Reorder the factors of $(x + 3) (4 (x - 3))$ .

$\frac{5}{4 (x + 3) (x - 3)} + \frac{2 (4 (x - 3))}{4 (x + 3) (x - 3)}$

Combine the numerators over the common denominator.

$\frac{5 + 2 (4 (x - 3))}{4 (x + 3) (x - 3)}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{5 + 8 (x - 3)}{4 (x + 3) (x - 3)}$

Apply the distributive property.

$\frac{5 + 8 x + 8 \cdot - 3}{4 (x + 3) (x - 3)}$

Multiply $8$ by $- 3$ .

$\frac{5 + 8 x - 24}{4 (x + 3) (x - 3)}$

Subtract $24$ from $5$ .

$\frac{8 x - 19}{4 (x + 3) (x - 3)}$

Simplify 5/(4x^2-36)+4/(2x+6)

Related Questions

Support LCMGCF.com by disabling your adblocker.