Solve the Rational Equation for x (2x+1)/(4x-5)=3

$\frac{2 x + 1}{4 x - 5} = 3$

Step 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.

$4 x - 5, 1$

Remove parentheses.

$4 x - 5, 1$

The LCM of one and any expression is the expression.

$4 x - 5$

Step 2

Multiply each term in $\frac{2 x + 1}{4 x - 5} = 3$ by $4 x - 5$ to eliminate the fractions.

Multiply each term in $\frac{2 x + 1}{4 x - 5} = 3$ by $4 x - 5$ .

$\frac{2 x + 1}{4 x - 5} (4 x - 5) = 3 (4 x - 5)$

Simplify the left side.

Cancel the common factor of $4 x - 5$ .

Cancel the common factor.

$\frac{2 x + 1}{4 x - 5} (4 x - 5) = 3 (4 x - 5)$

Rewrite the expression.

$2 x + 1 = 3 (4 x - 5)$

Simplify the right side.

Apply the distributive property.

$2 x + 1 = 3 (4 x) + 3 \cdot - 5$

Multiply.

Multiply $4$ by $3$ .

$2 x + 1 = 12 x + 3 \cdot - 5$

Multiply $3$ by $- 5$ .

$2 x + 1 = 12 x - 15$

Step 3

Solve the equation.

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

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

$2 x + 1 - 12 x = - 15$

Subtract $12 x$ from $2 x$ .

$- 10 x + 1 = - 15$

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

Subtract $1$ from both sides of the equation.

$- 10 x = - 15 - 1$

Subtract $1$ from $- 15$ .

$- 10 x = - 16$

Divide each term in $- 10 x = - 16$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 16$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 16}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 16}{- 10}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 10}$

Simplify the right side.

Cancel the common factor of $- 16$ and $- 10$ .

Factor $- 2$ out of $- 16$ .

$x = \frac{- 2 (8)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$x = \frac{- 2 \cdot 8}{- 2 \cdot 5}$

Cancel the common factor.

$x = \frac{- 2 \cdot 8}{- 2 \cdot 5}$

Rewrite the expression.

$x = \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{5}$

Decimal Form:

$x = 1.6$

Mixed Number Form:

$x = 1 \frac{3}{5}$

Solve the Rational Equation for x (2x+1)/(4x-5)=3

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