Solve by Factoring x+12/x=7

$x + \frac{12}{x} = 7$

Step 1

Subtract $7$ from both sides of the equation.

$x + \frac{12}{x} - 7 = 0$

Step 2

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

$\frac{x \cdot x}{x} + \frac{12}{x} - 7 = 0$

Step 3

Combine the numerators over the common denominator.

$\frac{x \cdot x + 12}{x} - 7 = 0$

Step 4

Multiply $x$ by $x$ .

$\frac{x^{2} + 12}{x} - 7 = 0$

Step 5

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

$\frac{x^{2} + 12}{x} - 7 \cdot \frac{x}{x} = 0$

Step 6

Combine $- 7$ and $\frac{x}{x}$ .

$\frac{x^{2} + 12}{x} + \frac{- 7 x}{x} = 0$

Step 7

Combine the numerators over the common denominator.

$\frac{x^{2} + 12 - 7 x}{x} = 0$

Step 8

Factor $x^{2} + 12 - 7 x$ 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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Write the factored form using these integers.

$\frac{(x - 4) (x - 3)}{x} = 0$

Step 9

Set the numerator equal to zero.

$(x - 4) (x - 3) = 0$

Step 10

Solve the equation for $x$ .

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

$x - 4 = 0$

$x - 3 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The final solution is all the values that make $(x - 4) (x - 3) = 0$ true.

$x = 4, 3$

Solve by Factoring x+12/x=7

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