Solve by Factoring x/3=-2/(x+7)

$\frac{x}{3} = \frac{- 2}{x + 7}$

Step 1

Subtract $\frac{- 2}{x + 7}$ from both sides of the equation.

$\frac{x}{3} - \frac{- 2}{x + 7} = 0$

Step 2

Simplify $\frac{x}{3} - \frac{- 2}{x + 7}$ .

Simplify each term.

Move the negative in front of the fraction.

$\frac{x}{3} - - \frac{2}{x + 7} = 0$

Multiply $- - \frac{2}{x + 7}$ .

Multiply $- 1$ by $- 1$ .

$\frac{x}{3} + 1 \frac{2}{x + 7} = 0$

Multiply $\frac{2}{x + 7}$ by $1$ .

$\frac{x}{3} + \frac{2}{x + 7} = 0$

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{x}{3} \cdot \frac{x + 7}{x + 7} + \frac{2}{x + 7} = 0$

To write $\frac{2}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{x + 7}{x + 7} + \frac{2}{x + 7} \cdot \frac{3}{3} = 0$

Write each expression with a common denominator of $3 (x + 7)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3}$ by $\frac{x + 7}{x + 7}$ .

$\frac{x (x + 7)}{3 (x + 7)} + \frac{2}{x + 7} \cdot \frac{3}{3} = 0$

Multiply $\frac{2}{x + 7}$ by $\frac{3}{3}$ .

$\frac{x (x + 7)}{3 (x + 7)} + \frac{2 \cdot 3}{(x + 7) \cdot 3} = 0$

Reorder the factors of $(x + 7) \cdot 3$ .

$\frac{x (x + 7)}{3 (x + 7)} + \frac{2 \cdot 3}{3 (x + 7)} = 0$

Combine the numerators over the common denominator.

$\frac{x (x + 7) + 2 \cdot 3}{3 (x + 7)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot x + x \cdot 7 + 2 \cdot 3}{3 (x + 7)} = 0$

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot 7 + 2 \cdot 3}{3 (x + 7)} = 0$

Move $7$ to the left of $x$ .

$\frac{x^{2} + 7 \cdot x + 2 \cdot 3}{3 (x + 7)} = 0$

Multiply $2$ by $3$ .

$\frac{x^{2} + 7 x + 6}{3 (x + 7)} = 0$

Factor $x^{2} + 7 x + 6$ 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 $7$ .

$1, 6$

Write the factored form using these integers.

$\frac{(x + 1) (x + 6)}{3 (x + 7)} = 0$

Step 3

Set the numerator equal to zero.

$(x + 1) (x + 6) = 0$

Step 4

Solve the equation for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 1 = 0$

$x + 6 = 0$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x + 1) (x + 6) = 0$ true.

$x = - 1, - 6$

Solve by Factoring x/3=-2/(x+7)

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