Find the Excluded Values 40/(x-4)+7=3/(x-4)

$\frac{40}{x - 4} + 7 = \frac{3}{x - 4}$

Step 1

Subtract $\frac{3}{x - 4}$ from both sides of the equation.

$\frac{40}{x - 4} + 7 - \frac{3}{x - 4} = 0$

Step 2

Simplify $\frac{40}{x - 4} + 7 - \frac{3}{x - 4}$ .

Combine the numerators over the common denominator.

$7 + \frac{40 - 3}{x - 4} = 0$

Subtract $3$ from $40$ .

$7 + \frac{37}{x - 4} = 0$

To write $7$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{7 (x - 4)}{x - 4} + \frac{37}{x - 4} = 0$

Combine the numerators over the common denominator.

$\frac{7 (x - 4) + 37}{x - 4} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{7 x + 7 \cdot - 4 + 37}{x - 4} = 0$

Multiply $7$ by $- 4$ .

$\frac{7 x - 28 + 37}{x - 4} = 0$

Add $- 28$ and $37$ .

$\frac{7 x + 9}{x - 4} = 0$

Step 3

Set the denominator in $\frac{7 x + 9}{x - 4}$ equal to $0$ to find where the expression is undefined.

$x - 4 = 0$

Step 4

Add $4$ to both sides of the equation.

$x = 4$

Step 5