Solve by Factoring x+9/x=-10

$x + \frac{9}{x} = - 10$

Step 1

Add $10$ to both sides of the equation.

$x + \frac{9}{x} + 10 = 0$

Step 2

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

$\frac{x \cdot x}{x} + \frac{9}{x} + 10 = 0$

Step 3

Combine the numerators over the common denominator.

$\frac{x \cdot x + 9}{x} + 10 = 0$

Step 4

Multiply $x$ by $x$ .

$\frac{x^{2} + 9}{x} + 10 = 0$

Step 5

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

$\frac{x^{2} + 9}{x} + \frac{10 x}{x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{x^{2} + 9 + 10 x}{x} = 0$

Step 7

Factor $x^{2} + 9 + 10 x$ 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 $9$ and whose sum is $10$ .

$1, 9$

Write the factored form using these integers.

$\frac{(x + 1) (x + 9)}{x} = 0$

Step 8

Set the numerator equal to zero.

$(x + 1) (x + 9) = 0$

Step 9

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 $0$ .

$x + 1 = 0$

$x + 9 = 0$

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 $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $(x + 1) (x + 9) = 0$ true.

$x = - 1, - 9$

Solve by Factoring x+9/x=-10

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