Solve the Rational Equation for x (25-3x)/(x+5)=1

$\frac{25 - 3 x}{x + 5} = 1$

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.

$x + 5, 1$

Remove parentheses.

$x + 5, 1$

The LCM of one and any expression is the expression.

$x + 5$

Multiply each term in $\frac{25 - 3 x}{x + 5} = 1$ by $x + 5$ to eliminate the fractions.

Multiply each term in $\frac{25 - 3 x}{x + 5} = 1$ by $x + 5$ .

$\frac{25 - 3 x}{x + 5} (x + 5) = 1 (x + 5)$

Simplify the left side.

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{25 - 3 x}{x + 5} (x + 5) = 1 (x + 5)$

Rewrite the expression.

$25 - 3 x = 1 (x + 5)$

Simplify the right side.

Multiply $x + 5$ by $1$ .

$25 - 3 x = x + 5$

Solve the equation.

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

Subtract $x$ from both sides of the equation.

$25 - 3 x - x = 5$

Subtract $x$ from $- 3 x$ .

$25 - 4 x = 5$

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

Subtract $25$ from both sides of the equation.

$- 4 x = 5 - 25$

Subtract $25$ from $5$ .

$- 4 x = - 20$

Divide each term in $- 4 x = - 20$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 20$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 20}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 20}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 20}{- 4}$

Simplify the right side.

Divide $- 20$ by $- 4$ .

$x = 5$