Solve by Factoring t+2/t=-3

$t + \frac{2}{t} = - 3$

Step 1

Add $3$ to both sides of the equation.

$t + \frac{2}{t} + 3 = 0$

Step 2

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

$\frac{t \cdot t}{t} + \frac{2}{t} + 3 = 0$

Step 3

Combine the numerators over the common denominator.

$\frac{t \cdot t + 2}{t} + 3 = 0$

Step 4

Multiply $t$ by $t$ .

$\frac{t^{2} + 2}{t} + 3 = 0$

Step 5

To write $3$ as a fraction with a common denominator, multiply by $\frac{t}{t}$ .

$\frac{t^{2} + 2}{t} + \frac{3 t}{t} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{t^{2} + 2 + 3 t}{t} = 0$

Step 7

Factor $t^{2} + 2 + 3 t$ 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 $2$ and whose sum is $3$ .

$1, 2$

Write the factored form using these integers.

$\frac{(t + 1) (t + 2)}{t} = 0$

Step 8

Set the numerator equal to zero.

$(t + 1) (t + 2) = 0$

Step 9

Solve the equation for $t$ .

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

$t + 1 = 0$

$t + 2 = 0$

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

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

$t + 1 = 0$

Subtract $1$ from both sides of the equation.

$t = - 1$

Set $t + 2$ equal to $0$ and solve for $t$ .

Set $t + 2$ equal to $0$ .

$t + 2 = 0$

Subtract $2$ from both sides of the equation.

$t = - 2$

The final solution is all the values that make $(t + 1) (t + 2) = 0$ true.

$t = - 1, - 2$

Solve by Factoring t+2/t=-3

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