Solve by Factoring y+6/y=-7

$y + \frac{6}{y} = - 7$

Step 1

Add $7$ to both sides of the equation.

$y + \frac{6}{y} + 7 = 0$

Step 2

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

$\frac{y \cdot y}{y} + \frac{6}{y} + 7 = 0$

Step 3

Combine the numerators over the common denominator.

$\frac{y \cdot y + 6}{y} + 7 = 0$

Step 4

Multiply $y$ by $y$ .

$\frac{y^{2} + 6}{y} + 7 = 0$

Step 5

To write $7$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{y^{2} + 6}{y} + \frac{7 y}{y} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{y^{2} + 6 + 7 y}{y} = 0$

Step 7

Factor $y^{2} + 6 + 7 y$ 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 $6$ and whose sum is $7$ .

$1, 6$

Write the factored form using these integers.

$\frac{(y + 1) (y + 6)}{y} = 0$

Step 8

Set the numerator equal to zero.

$(y + 1) (y + 6) = 0$

Step 9

Solve the equation for $y$ .

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

$y + 1 = 0$

$y + 6 = 0$

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

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

$y + 1 = 0$

Subtract $1$ from both sides of the equation.

$y = - 1$

Set $y + 6$ equal to $0$ and solve for $y$ .

Set $y + 6$ equal to $0$ .

$y + 6 = 0$

Subtract $6$ from both sides of the equation.

$y = - 6$

The final solution is all the values that make $(y + 1) (y + 6) = 0$ true.

$y = - 1, - 6$

Solve by Factoring y+6/y=-7

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