Solve by Factoring 10/(x+3)+10/3=6

$\frac{10}{x + 3} + \frac{10}{3} = 6$

Step 1

Subtract $6$ from both sides of the equation.

$\frac{10}{x + 3} + \frac{10}{3} - 6 = 0$

Step 2

Simplify $\frac{10}{x + 3} + \frac{10}{3} - 6$ .

To write $\frac{10}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10}{x + 3} \cdot \frac{3}{3} + \frac{10}{3} - 6 = 0$

To write $\frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{10}{x + 3} \cdot \frac{3}{3} + \frac{10}{3} \cdot \frac{x + 3}{x + 3} - 6 = 0$

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

Multiply $\frac{10}{x + 3}$ by $\frac{3}{3}$ .

$\frac{10 \cdot 3}{(x + 3) \cdot 3} + \frac{10}{3} \cdot \frac{x + 3}{x + 3} - 6 = 0$

Multiply $\frac{10}{3}$ by $\frac{x + 3}{x + 3}$ .

$\frac{10 \cdot 3}{(x + 3) \cdot 3} + \frac{10 (x + 3)}{3 (x + 3)} - 6 = 0$

Reorder the factors of $(x + 3) \cdot 3$ .

$\frac{10 \cdot 3}{3 (x + 3)} + \frac{10 (x + 3)}{3 (x + 3)} - 6 = 0$

Combine the numerators over the common denominator.

$\frac{10 \cdot 3 + 10 (x + 3)}{3 (x + 3)} - 6 = 0$

Multiply $10$ by $3$ .

$\frac{30 + 10 (x + 3)}{3 (x + 3)} - 6 = 0$

Simplify the numerator.

Factor $10$ out of $30 + 10 (x + 3)$ .

Factor $10$ out of $30$ .

$\frac{10 \cdot 3 + 10 (x + 3)}{3 (x + 3)} - 6 = 0$

Factor $10$ out of $10 \cdot 3 + 10 (x + 3)$ .

$\frac{10 (3 + x + 3)}{3 (x + 3)} - 6 = 0$

Add $3$ and $3$ .

$\frac{10 (x + 6)}{3 (x + 3)} - 6 = 0$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{3 (x + 3)}{3 (x + 3)}$ .

$\frac{10 (x + 6)}{3 (x + 3)} - 6 \cdot \frac{3 (x + 3)}{3 (x + 3)} = 0$

Combine $- 6$ and $\frac{3 (x + 3)}{3 (x + 3)}$ .

$\frac{10 (x + 6)}{3 (x + 3)} + \frac{- 6 (3 (x + 3))}{3 (x + 3)} = 0$

Combine the numerators over the common denominator.

$\frac{10 (x + 6) - 6 (3 (x + 3))}{3 (x + 3)} = 0$

Simplify the numerator.

Factor $2$ out of $10 (x + 6) - 6 \cdot 3 (x + 3)$ .

Factor $2$ out of $10 (x + 6)$ .

$\frac{2 (5 (x + 6)) - 6 \cdot 3 (x + 3)}{3 (x + 3)} = 0$

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

$\frac{2 (5 (x + 6)) + 2 (- 3 \cdot 3 (x + 3))}{3 (x + 3)} = 0$

Factor $2$ out of $2 (5 (x + 6)) + 2 (- 3 \cdot 3 (x + 3))$ .

$\frac{2 (5 (x + 6) - 3 \cdot 3 (x + 3))}{3 (x + 3)} = 0$

Apply the distributive property.

$\frac{2 (5 x + 5 \cdot 6 - 3 \cdot 3 (x + 3))}{3 (x + 3)} = 0$

Multiply $5$ by $6$ .

$\frac{2 (5 x + 30 - 3 \cdot 3 (x + 3))}{3 (x + 3)} = 0$

Multiply $- 3$ by $3$ .

$\frac{2 (5 x + 30 - 9 (x + 3))}{3 (x + 3)} = 0$

Apply the distributive property.

$\frac{2 (5 x + 30 - 9 x - 9 \cdot 3)}{3 (x + 3)} = 0$

Multiply $- 9$ by $3$ .

$\frac{2 (5 x + 30 - 9 x - 27)}{3 (x + 3)} = 0$

Subtract $9 x$ from $5 x$ .

$\frac{2 (- 4 x + 30 - 27)}{3 (x + 3)} = 0$

Subtract $27$ from $30$ .

$\frac{2 (- 4 x + 3)}{3 (x + 3)} = 0$

Factor $- 1$ out of $- 4 x$ .

$\frac{2 (- (4 x) + 3)}{3 (x + 3)} = 0$

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{2 (- (4 x) - 1 (- 3))}{3 (x + 3)} = 0$

Factor $- 1$ out of $- (4 x) - 1 (- 3)$ .

$\frac{2 (- (4 x - 3))}{3 (x + 3)} = 0$

Rewrite $- (4 x - 3)$ as $- 1 (4 x - 3)$ .

$\frac{2 (- 1 (4 x - 3))}{3 (x + 3)} = 0$

Move the negative in front of the fraction.

$- \frac{2 (4 x - 3)}{3 (x + 3)} = 0$

Step 3

Set the numerator equal to zero.

$2 (4 x - 3) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (4 x - 3) = 0$ by $2$ and simplify.

Divide each term in $2 (4 x - 3) = 0$ by $2$ .

$\frac{2 (4 x - 3)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (4 x - 3)}{2} = \frac{0}{2}$

Divide $4 x - 3$ by $1$ .

$4 x - 3 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$4 x - 3 = 0$

Add $3$ to both sides of the equation.

$4 x = 3$

Divide each term in $4 x = 3$ by $4$ and simplify.

Divide each term in $4 x = 3$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$

Solve by Factoring 10/(x+3)+10/3=6

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