Solve for x (x-2)/3-(x-3)/4=(x-4)/5

$\frac{x - 2}{3} - \frac{x - 3}{4} = \frac{x - 4}{5}$

Multiply both sides by $5$ .

$(\frac{x - 2}{3} - \frac{x - 3}{4}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

Simplify.

Simplify the left side.

Simplify $(\frac{x - 2}{3} - \frac{x - 3}{4}) \cdot 5$ .

To write $\frac{x - 2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{x - 2}{3} \cdot \frac{4}{4} - \frac{x - 3}{4}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

To write $- \frac{x - 3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{x - 2}{3} \cdot \frac{4}{4} - \frac{x - 3}{4} \cdot \frac{3}{3}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 2}{3}$ by $\frac{4}{4}$ .

$(\frac{(x - 2) \cdot 4}{3 \cdot 4} - \frac{x - 3}{4} \cdot \frac{3}{3}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $3$ by $4$ .

$(\frac{(x - 2) \cdot 4}{12} - \frac{x - 3}{4} \cdot \frac{3}{3}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $\frac{x - 3}{4}$ by $\frac{3}{3}$ .

$(\frac{(x - 2) \cdot 4}{12} - \frac{(x - 3) \cdot 3}{4 \cdot 3}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $4$ by $3$ .

$(\frac{(x - 2) \cdot 4}{12} - \frac{(x - 3) \cdot 3}{12}) \cdot 5 = \frac{x - 4}{5} \cdot 5$

Combine the numerators over the common denominator.

$\frac{(x - 2) \cdot 4 - (x - 3) \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 4 - 2 \cdot 4 - (x - 3) \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Move $4$ to the left of $x$ .

$\frac{4 \cdot x - 2 \cdot 4 - (x - 3) \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $- 2$ by $4$ .

$\frac{4 \cdot x - 8 - (x - 3) \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Apply the distributive property.

$\frac{4 x - 8 + (- x - - 3) \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $- 1$ by $- 3$ .

$\frac{4 x - 8 + (- x + 3) \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Apply the distributive property.

$\frac{4 x - 8 - x \cdot 3 + 3 \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $3$ by $- 1$ .

$\frac{4 x - 8 - 3 x + 3 \cdot 3}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Multiply $3$ by $3$ .

$\frac{4 x - 8 - 3 x + 9}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Subtract $3 x$ from $4 x$ .

$\frac{x - 8 + 9}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Add $- 8$ and $9$ .

$\frac{x + 1}{12} \cdot 5 = \frac{x - 4}{5} \cdot 5$

Combine fractions.

Combine $\frac{x + 1}{12}$ and $5$ .

$\frac{(x + 1) \cdot 5}{12} = \frac{x - 4}{5} \cdot 5$

Move $5$ to the left of $x + 1$ .

$\frac{5 (x + 1)}{12} = \frac{x - 4}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (x + 1)}{12} = \frac{x - 4}{5} \cdot 5$

Rewrite the expression.

$\frac{5 (x + 1)}{12} = x - 4$

Solve for $x$ .

Multiply both sides by $12$ .

$\frac{5 (x + 1)}{12} \cdot 12 = (x - 4) \cdot 12$

Simplify.

Simplify the left side.

Simplify $\frac{5 (x + 1)}{12} \cdot 12$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{5 (x + 1)}{12} \cdot 12 = (x - 4) \cdot 12$

Rewrite the expression.

$5 (x + 1) = (x - 4) \cdot 12$

Apply the distributive property.

$5 x + 5 \cdot 1 = (x - 4) \cdot 12$

Multiply $5$ by $1$ .

$5 x + 5 = (x - 4) \cdot 12$

Simplify the right side.

Simplify $(x - 4) \cdot 12$ .

Apply the distributive property.

$5 x + 5 = x \cdot 12 - 4 \cdot 12$

Simplify the expression.

Move $12$ to the left of $x$ .

$5 x + 5 = 12 \cdot x - 4 \cdot 12$

Multiply $- 4$ by $12$ .

$5 x + 5 = 12 x - 48$

Solve for $x$ .

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

Subtract $12 x$ from both sides of the equation.

$5 x + 5 - 12 x = - 48$

Subtract $12 x$ from $5 x$ .

$- 7 x + 5 = - 48$

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

Subtract $5$ from both sides of the equation.

$- 7 x = - 48 - 5$

Subtract $5$ from $- 48$ .

$- 7 x = - 53$

Divide each term in $- 7 x = - 53$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 53$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 53}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 53}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 53}{- 7}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{53}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{53}{7}$

Decimal Form:

$x = 7.\overline{571428}$

Mixed Number Form:

$x = 7 \frac{4}{7}$

Solve for x (x-2)/3-(x-3)/4=(x-4)/5

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