Solve by Factoring m+12/m=7

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

Step 1

Subtract $7$ from both sides of the equation.

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Multiply $m$ by $m$ .

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

Step 5

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

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

Step 6

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

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Factor $m^{2} + 12 - 7 m$ 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.

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

Step 9

Set the numerator equal to zero.

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

Step 10

Solve the equation for $m$ .

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

$m - 4 = 0$

$m - 3 = 0$

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

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

$m - 4 = 0$

Add $4$ to both sides of the equation.

$m = 4$

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

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

$m - 3 = 0$

Add $3$ to both sides of the equation.

$m = 3$

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

$m = 4, 3$

Solve by Factoring m+12/m=7

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