Simplify 5/(x^2)-3/(6x^2+12x)

$\frac{5}{x^{2}} - \frac{3}{6 x^{2} + 12 x}$

Step 1

Simplify each term.

Factor $6 x$ out of $6 x^{2} + 12 x$ .

Factor $6 x$ out of $6 x^{2}$ .

$\frac{5}{x^{2}} - \frac{3}{6 x (x) + 12 x}$

Factor $6 x$ out of $12 x$ .

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

Factor $6 x$ out of $6 x (x) + 6 x (2)$ .

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

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$\frac{5}{x^{2}} - \frac{3 (1)}{6 x (x + 2)}$

Cancel the common factors.

Factor $3$ out of $6 x (x + 2)$ .

$\frac{5}{x^{2}} - \frac{3 (1)}{3 (2 x (x + 2))}$

Cancel the common factor.

$\frac{5}{x^{2}} - \frac{3 \cdot 1}{3 (2 x (x + 2))}$

Rewrite the expression.

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

Step 2

To write $\frac{5}{x^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 (x + 2)}{2 (x + 2)}$ .

$\frac{5}{x^{2}} \cdot \frac{2 (x + 2)}{2 (x + 2)} - \frac{1}{2 x (x + 2)}$

Step 3

To write $- \frac{1}{2 x (x + 2)}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5}{x^{2}} \cdot \frac{2 (x + 2)}{2 (x + 2)} - \frac{1}{2 x (x + 2)} \cdot \frac{x}{x}$

Step 4

Write each expression with a common denominator of $2 (x + 2) x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{x^{2}}$ by $\frac{2 (x + 2)}{2 (x + 2)}$ .

$\frac{5 (2 (x + 2))}{x^{2} (2 (x + 2))} - \frac{1}{2 x (x + 2)} \cdot \frac{x}{x}$

Multiply $\frac{1}{2 x (x + 2)}$ by $\frac{x}{x}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Reorder the factors of $x^{2} (2 (x + 2))$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 (x + 2) - x}{2 x^{2} (x + 2)}$

Apply the distributive property.

$\frac{10 x + 10 \cdot 2 - x}{2 x^{2} (x + 2)}$

Multiply $10$ by $2$ .

$\frac{10 x + 20 - x}{2 x^{2} (x + 2)}$

Subtract $x$ from $10 x$ .

$\frac{9 x + 20}{2 x^{2} (x + 2)}$

Simplify 5/(x^2)-3/(6x^2+12x)

Related Questions

Support LCMGCF.com by disabling your adblocker.