Solve by Factoring 7/x+5/x=-4

$\frac{7}{x} + \frac{5}{x} = - 4$

Step 1

Add $4$ to both sides of the equation.

$\frac{7}{x} + \frac{5}{x} + 4 = 0$

Step 2

Simplify $\frac{7}{x} + \frac{5}{x} + 4$ .

Combine the numerators over the common denominator.

$4 + \frac{7 + 5}{x} = 0$

Add $7$ and $5$ .

$4 + \frac{12}{x} = 0$

Step 3

Factor $4$ out of $4 + \frac{12}{x}$ .

Factor $4$ out of $4$ .

$4 (1) + \frac{12}{x} = 0$

Factor $4$ out of $\frac{12}{x}$ .

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

Factor $4$ out of $4 \cdot 1 + 4 \frac{3}{x}$ .

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

Step 4

Write $1$ as a fraction with a common denominator.

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Combine $4$ and $\frac{x + 3}{x}$ .

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

Step 7

Set the numerator equal to zero.

$4 (x + 3) = 0$

Step 8

Solve the equation for $x$ .

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x + 3$ by $1$ .

$x + 3 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Solve by Factoring 7/x+5/x=-4

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