Solve for x x-8=-15/x

$x - 8 = - \frac{15}{x}$

Add $8$ to both sides of the equation.

$x = - \frac{15}{x} + 8$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $x = - \frac{15}{x} + 8$ by $x$ to eliminate the fractions.

Multiply each term in $x = - \frac{15}{x} + 8$ by $x$ .

$x \cdot x = - \frac{15}{x} x + 8 x$

Simplify the left side.

Multiply $x$ by $x$ .

$x^{2} = - \frac{15}{x} x + 8 x$

Simplify the right side.

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{15}{x}$ into the numerator.

$x^{2} = \frac{- 15}{x} x + 8 x$

Cancel the common factor.

$x^{2} = \frac{- 15}{x} x + 8 x$

Rewrite the expression.

$x^{2} = - 15 + 8 x$

Solve the equation.

Subtract $8 x$ from both sides of the equation.

$x^{2} - 8 x = - 15$

Add $15$ to both sides of the equation.

$x^{2} - 8 x + 15 = 0$

Factor $x^{2} - 8 x + 15$ 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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Write the factored form using these integers.

$(x - 5) (x - 3) = 0$

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

$x - 5 = 0$

$x - 3 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The final solution is all the values that make $(x - 5) (x - 3) = 0$ true.

$x = 5, 3$

Solve for x x-8=-15/x

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