Simplify (5k)/(k-2)-k/(k+2)

$\frac{5 k}{k - 2} - \frac{k}{k + 2}$

Step 1

To write $\frac{5 k}{k - 2}$ as a fraction with a common denominator, multiply by $\frac{k + 2}{k + 2}$ .

$\frac{5 k}{k - 2} \cdot \frac{k + 2}{k + 2} - \frac{k}{k + 2}$

Step 2

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

$\frac{5 k}{k - 2} \cdot \frac{k + 2}{k + 2} - \frac{k}{k + 2} \cdot \frac{k - 2}{k - 2}$

Step 3

Write each expression with a common denominator of $(k - 2) (k + 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 k}{k - 2}$ by $\frac{k + 2}{k + 2}$ .

$\frac{5 k (k + 2)}{(k - 2) (k + 2)} - \frac{k}{k + 2} \cdot \frac{k - 2}{k - 2}$

Multiply $\frac{k}{k + 2}$ by $\frac{k - 2}{k - 2}$ .

$\frac{5 k (k + 2)}{(k - 2) (k + 2)} - \frac{k (k - 2)}{(k + 2) (k - 2)}$

Reorder the factors of $(k - 2) (k + 2)$ .

$\frac{5 k (k + 2)}{(k + 2) (k - 2)} - \frac{k (k - 2)}{(k + 2) (k - 2)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 k (k + 2) - k (k - 2)}{(k + 2) (k - 2)}$

Step 5

Simplify the numerator.

Factor $k$ out of $5 k (k + 2) - k (k - 2)$ .

Factor $k$ out of $5 k (k + 2)$ .

$\frac{k (5 (k + 2)) - k (k - 2)}{(k + 2) (k - 2)}$

Factor $k$ out of $- k (k - 2)$ .

$\frac{k (5 (k + 2)) + k (- (k - 2))}{(k + 2) (k - 2)}$

Factor $k$ out of $k (5 (k + 2)) + k (- (k - 2))$ .

$\frac{k (5 (k + 2) - (k - 2))}{(k + 2) (k - 2)}$

Apply the distributive property.

$\frac{k (5 k + 5 \cdot 2 - (k - 2))}{(k + 2) (k - 2)}$

Multiply $5$ by $2$ .

$\frac{k (5 k + 10 - (k - 2))}{(k + 2) (k - 2)}$

Apply the distributive property.

$\frac{k (5 k + 10 - k - - 2)}{(k + 2) (k - 2)}$

Multiply $- 1$ by $- 2$ .

$\frac{k (5 k + 10 - k + 2)}{(k + 2) (k - 2)}$

Subtract $k$ from $5 k$ .

$\frac{k (4 k + 10 + 2)}{(k + 2) (k - 2)}$

Add $10$ and $2$ .

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

Factor $4$ out of $4 k + 12$ .

Factor $4$ out of $4 k$ .

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

Factor $4$ out of $12$ .

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

Factor $4$ out of $4 k + 4 \cdot 3$ .

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

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

Step 6

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

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

Simplify (5k)/(k-2)-k/(k+2)

Related Questions

Support LCMGCF.com by disabling your adblocker.