Solve by Factoring x/3-88/(3x)=-1

$\frac{x}{3} - \frac{88}{3 x} = - 1$

Step 1

Add $1$ to both sides of the equation.

$\frac{x}{3} - \frac{88}{3 x} + 1 = 0$

Step 2

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

$\frac{x}{3} \cdot \frac{x}{x} - \frac{88}{3 x} + 1 = 0$

Step 3

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

$\frac{x \cdot x}{3 x} - \frac{88}{3 x} + 1 = 0$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot x - 88}{3 x} + 1 = 0$

Step 5

Multiply $x$ by $x$ .

$\frac{x^{2} - 88}{3 x} + 1 = 0$

Step 6

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

$\frac{x^{2} - 88}{3 x} + \frac{3 x}{3 x} = 0$

Step 7

Combine the numerators over the common denominator.

$\frac{x^{2} - 88 + 3 x}{3 x} = 0$

Step 8

Factor $x^{2} - 88 + 3 x$ 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 $- 88$ and whose sum is $3$ .

$- 8, 11$

Write the factored form using these integers.

$\frac{(x - 8) (x + 11)}{3 x} = 0$

Step 9

Set the numerator equal to zero.

$(x - 8) (x + 11) = 0$

Step 10

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 $0$ .

$x - 8 = 0$

$x + 11 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x + 11$ equal to $0$ and solve for $x$ .

Set $x + 11$ equal to $0$ .

$x + 11 = 0$

Subtract $11$ from both sides of the equation.

$x = - 11$

The final solution is all the values that make $(x - 8) (x + 11) = 0$ true.

$x = 8, - 11$

Solve by Factoring x/3-88/(3x)=-1

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