Solve by Factoring y-10/y=3

$y - \frac{10}{y} = 3$

Step 1

Subtract $3$ from both sides of the equation.

$y - \frac{10}{y} - 3 = 0$

Step 2

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

$\frac{y \cdot y}{y} - \frac{10}{y} - 3 = 0$

Step 3

Combine the numerators over the common denominator.

$\frac{y \cdot y - 10}{y} - 3 = 0$

Step 4

Multiply $y$ by $y$ .

$\frac{y^{2} - 10}{y} - 3 = 0$

Step 5

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

$\frac{y^{2} - 10}{y} - 3 \cdot \frac{y}{y} = 0$

Step 6

Combine $- 3$ and $\frac{y}{y}$ .

$\frac{y^{2} - 10}{y} + \frac{- 3 y}{y} = 0$

Step 7

Combine the numerators over the common denominator.

$\frac{y^{2} - 10 - 3 y}{y} = 0$

Step 8

Factor $y^{2} - 10 - 3 y$ 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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$\frac{(y - 5) (y + 2)}{y} = 0$

Step 9

Set the numerator equal to zero.

$(y - 5) (y + 2) = 0$

Step 10

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 $0$ .

$y - 5 = 0$

$y + 2 = 0$

Set $y - 5$ equal to $0$ and solve for $y$ .

Set $y - 5$ equal to $0$ .

$y - 5 = 0$

Add $5$ to both sides of the equation.

$y = 5$

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

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

$y + 2 = 0$

Subtract $2$ from both sides of the equation.

$y = - 2$

The final solution is all the values that make $(y - 5) (y + 2) = 0$ true.

$y = 5, - 2$

Solve by Factoring y-10/y=3

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