Solve for x (x-3)/(x-4)+4=(3x)/x

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

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{3 x}{x}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 3}{x - 4} + 4 = \frac{3}{1}$

Divide $3$ by $1$ .

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

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 4, 1, 1$

Remove parentheses.

$x - 4, 1, 1$

The LCM of one and any expression is the expression.

$x - 4$

Multiply each term in $\frac{x - 3}{x - 4} + 4 = 3$ by $x - 4$ to eliminate the fractions.

Multiply each term in $\frac{x - 3}{x - 4} + 4 = 3$ by $x - 4$ .

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

Simplify the left side.

Simplify each term.

Cancel the common factor of $x - 4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

$x - 3 + 4 x + 4 \cdot - 4 = 3 (x - 4)$

Multiply $4$ by $- 4$ .

$x - 3 + 4 x - 16 = 3 (x - 4)$

Simplify by adding terms.

Add $x$ and $4 x$ .

$5 x - 3 - 16 = 3 (x - 4)$

Subtract $16$ from $- 3$ .

$5 x - 19 = 3 (x - 4)$

Simplify the right side.

Apply the distributive property.

$5 x - 19 = 3 x + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$5 x - 19 = 3 x - 12$

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$5 x - 19 - 3 x = - 12$

Subtract $3 x$ from $5 x$ .

$2 x - 19 = - 12$

Move all terms not containing $x$ to the right side of the equation.

Add $19$ to both sides of the equation.

$2 x = - 12 + 19$

Add $- 12$ and $19$ .

$2 x = 7$

Divide each term in $2 x = 7$ by $2$ and simplify.

Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

$x = 3 \frac{1}{2}$

Solve for x (x-3)/(x-4)+4=(3x)/x

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