Solve for x x-15/x=2

$x - \frac{15}{x} = 2$

Step 1

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.

$x$

Step 2

Multiply each term in $x - \frac{15}{x} = 2$ by $x$ to eliminate the fractions.

Multiply each term in $x - \frac{15}{x} = 2$ by $x$ .

$x \cdot x - \frac{15}{x} x = 2 x$

Simplify the left side.

Simplify each term.

Multiply $x$ by $x$ .

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

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Solve the equation.

Subtract $2 x$ from both sides of the equation.

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

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

$- 5, 3$

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 $0$ .

$x + 3 = 0$

Subtract $3$ from 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-15/x=2

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