Solve for s s+7/s=-8

$s + \frac{7}{s} = - 8$

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.

$1, s, 1$

The LCM of one and any expression is the expression.

$s$

Multiply each term in $s + \frac{7}{s} = - 8$ by $s$ to eliminate the fractions.

Multiply each term in $s + \frac{7}{s} = - 8$ by $s$ .

$s \cdot s + \frac{7}{s} s = - 8 s$

Simplify the left side.

Simplify each term.

Multiply $s$ by $s$ .

$s^{2} + \frac{7}{s} s = - 8 s$

Cancel the common factor of $s$ .

Cancel the common factor.

$s^{2} + \frac{7}{s} s = - 8 s$

Rewrite the expression.

$s^{2} + 7 = - 8 s$

Solve the equation.

Add $8 s$ to both sides of the equation.

$s^{2} + 7 + 8 s = 0$

Factor $s^{2} + 7 + 8 s$ 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 $7$ and whose sum is $8$ .

$1, 7$

Write the factored form using these integers.

$(s + 1) (s + 7) = 0$

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

$s + 1 = 0$

$s + 7 = 0$

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

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

$s + 1 = 0$

Subtract $1$ from both sides of the equation.

$s = - 1$

Set $s + 7$ equal to $0$ and solve for $s$ .

Set $s + 7$ equal to $0$ .

$s + 7 = 0$

Subtract $7$ from both sides of the equation.

$s = - 7$

The final solution is all the values that make $(s + 1) (s + 7) = 0$ true.

$s = - 1, - 7$

Solve for s s+7/s=-8

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