Solve for p p+9/p=-10

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

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.

$1, p, 1$

The LCM of one and any expression is the expression.

$p$

Multiply each term in $p + \frac{9}{p} = - 10$ by $p$ to eliminate the fractions.

Multiply each term in $p + \frac{9}{p} = - 10$ by $p$ .

$p \cdot p + \frac{9}{p} p = - 10 p$

Simplify the left side.

Simplify each term.

Multiply $p$ by $p$ .

$p^{2} + \frac{9}{p} p = - 10 p$

Cancel the common factor of $p$ .

Cancel the common factor.

$p^{2} + \frac{9}{p} p = - 10 p$

Rewrite the expression.

$p^{2} + 9 = - 10 p$

Solve the equation.

Add $10 p$ to both sides of the equation.

$p^{2} + 9 + 10 p = 0$

Factor $p^{2} + 9 + 10 p$ 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.

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

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

$p + 1 = 0$

$p + 9 = 0$

Set $p + 1$ equal to $0$ and solve for $p$ .

Set $p + 1$ equal to $0$ .

$p + 1 = 0$

Subtract $1$ from both sides of the equation.

$p = - 1$

Set $p + 9$ equal to $0$ and solve for $p$ .

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

$p + 9 = 0$

Subtract $9$ from both sides of the equation.

$p = - 9$

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

$p = - 1, - 9$

Solve for p p+9/p=-10

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