Solve by Factoring 2/x+3=5/(4x)+25/8

$\frac{2}{x} + 3 = \frac{5}{4 x} + \frac{25}{8}$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{5}{4 x}$ from both sides of the equation.

$\frac{2}{x} + 3 - \frac{5}{4 x} = \frac{25}{8}$

Subtract $\frac{25}{8}$ from both sides of the equation.

$\frac{2}{x} + 3 - \frac{5}{4 x} - \frac{25}{8} = 0$

Step 2

Simplify $\frac{2}{x} + 3 - \frac{5}{4 x} - \frac{25}{8}$ .

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

$\frac{2}{x} \cdot \frac{4}{4} - \frac{5}{4 x} + 3 - \frac{25}{8} = 0$

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2 \cdot 4}{x \cdot 4} - \frac{5}{4 x} + 3 - \frac{25}{8} = 0$

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

$\frac{2 \cdot 4}{4 x} - \frac{5}{4 x} + 3 - \frac{25}{8} = 0$

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 - 5}{4 x} + 3 - \frac{25}{8} = 0$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{8 - 5}{4 x} + 3 - \frac{25}{8} = 0$

Subtract $5$ from $8$ .

$\frac{3}{4 x} + 3 - \frac{25}{8} = 0$

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3}{4 x} + 3 \cdot \frac{8}{8} - \frac{25}{8} = 0$

Combine $3$ and $\frac{8}{8}$ .

$\frac{3}{4 x} + \frac{3 \cdot 8}{8} - \frac{25}{8} = 0$

Combine the numerators over the common denominator.

$\frac{3}{4 x} + \frac{3 \cdot 8 - 25}{8} = 0$

Simplify the numerator.

Multiply $3$ by $8$ .

$\frac{3}{4 x} + \frac{24 - 25}{8} = 0$

Subtract $25$ from $24$ .

$\frac{3}{4 x} + \frac{- 1}{8} = 0$

Move the negative in front of the fraction.

$\frac{3}{4 x} - \frac{1}{8} = 0$

Step 3

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

$\frac{3}{4 x} \cdot \frac{2}{2} - \frac{1}{8} = 0$

Step 4

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3}{4 x} \cdot \frac{2}{2} - \frac{1}{8} \cdot \frac{x}{x} = 0$

Step 5

Write each expression with a common denominator of $8 x$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 \cdot 2}{4 x \cdot 2} - \frac{1}{8} \cdot \frac{x}{x} = 0$

Multiply $2$ by $4$ .

$\frac{3 \cdot 2}{8 x} - \frac{1}{8} \cdot \frac{x}{x} = 0$

Multiply $\frac{1}{8}$ by $\frac{x}{x}$ .

$\frac{3 \cdot 2}{8 x} - \frac{x}{8 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 - x}{8 x} = 0$

Step 7

Multiply $3$ by $2$ .

$\frac{6 - x}{8 x} = 0$

Step 8

Set the numerator equal to zero.

$6 - x = 0$

Step 9

Solve the equation for $x$ .

Subtract $6$ from both sides of the equation.

$- x = - 6$

Divide each term in $- x = - 6$ by $- 1$ and simplify.

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x = 6$

Solve by Factoring 2/x+3=5/(4x)+25/8

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