Solve by Factoring 2/(x+7)=4/x

$\frac{2}{x + 7} = \frac{4}{x}$

Step 1

Subtract $\frac{4}{x}$ from both sides of the equation.

$\frac{2}{x + 7} - \frac{4}{x} = 0$

Step 2

Simplify $\frac{2}{x + 7} - \frac{4}{x}$ .

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

$\frac{2}{x + 7} \cdot \frac{x}{x} - \frac{4}{x} = 0$

To write $- \frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{2}{x + 7} \cdot \frac{x}{x} - \frac{4}{x} \cdot \frac{x + 7}{x + 7} = 0$

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

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

$\frac{2 x}{(x + 7) x} - \frac{4}{x} \cdot \frac{x + 7}{x + 7} = 0$

Multiply $\frac{4}{x}$ by $\frac{x + 7}{x + 7}$ .

$\frac{2 x}{(x + 7) x} - \frac{4 (x + 7)}{x (x + 7)} = 0$

Reorder the factors of $(x + 7) x$ .

$\frac{2 x}{x (x + 7)} - \frac{4 (x + 7)}{x (x + 7)} = 0$

Combine the numerators over the common denominator.

$\frac{2 x - 4 (x + 7)}{x (x + 7)} = 0$

Simplify the numerator.

Factor $2$ out of $2 x - 4 (x + 7)$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 4 (x + 7)}{x (x + 7)} = 0$

Factor $2$ out of $- 4 (x + 7)$ .

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

Factor $2$ out of $2 (x) + 2 (- 2 (x + 7))$ .

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

Apply the distributive property.

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

Multiply $- 2$ by $7$ .

$\frac{2 (x - 2 x - 14)}{x (x + 7)} = 0$

Subtract $2 x$ from $x$ .

$\frac{2 (- x - 14)}{x (x + 7)} = 0$

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

$\frac{2 (- (x) - 14)}{x (x + 7)} = 0$

Rewrite $- 14$ as $- 1 (14)$ .

$\frac{2 (- (x) - 1 (14))}{x (x + 7)} = 0$

Factor $- 1$ out of $- (x) - 1 (14)$ .

$\frac{2 (- (x + 14))}{x (x + 7)} = 0$

Rewrite $- (x + 14)$ as $- 1 (x + 14)$ .

$\frac{2 (- 1 (x + 14))}{x (x + 7)} = 0$

Move the negative in front of the fraction.

$- \frac{2 (x + 14)}{x (x + 7)} = 0$

Step 3

Set the numerator equal to zero.

$2 (x + 14) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (x + 14) = 0$ by $2$ and simplify.

Divide each term in $2 (x + 14) = 0$ by $2$ .

$\frac{2 (x + 14)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x + 14)}{2} = \frac{0}{2}$

Divide $x + 14$ by $1$ .

$x + 14 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x + 14 = 0$

Subtract $14$ from both sides of the equation.

$x = - 14$

Solve by Factoring 2/(x+7)=4/x

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