Solve by Factoring 5/(2s)+3/4=9/(4s)

$\frac{5}{2 s} + \frac{3}{4} = \frac{9}{4 s}$

Step 1

Subtract $\frac{9}{4 s}$ from both sides of the equation.

$\frac{5}{2 s} + \frac{3}{4} - \frac{9}{4 s} = 0$

Step 2

Simplify $\frac{5}{2 s} + \frac{3}{4} - \frac{9}{4 s}$ .

To write $\frac{5}{2 s}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2 s} \cdot \frac{2}{2} - \frac{9}{4 s} + \frac{3}{4} = 0$

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

Multiply $\frac{5}{2 s}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{2 s \cdot 2} - \frac{9}{4 s} + \frac{3}{4} = 0$

Multiply $2$ by $2$ .

$\frac{5 \cdot 2}{4 s} - \frac{9}{4 s} + \frac{3}{4} = 0$

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 9}{4 s} + \frac{3}{4} = 0$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 - 9}{4 s} + \frac{3}{4} = 0$

Subtract $9$ from $10$ .

$\frac{1}{4 s} + \frac{3}{4} = 0$

Step 3

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

$\frac{1}{4 s} + \frac{3}{4} \cdot \frac{s}{s} = 0$

Step 4

Multiply $\frac{3}{4}$ by $\frac{s}{s}$ .

$\frac{1}{4 s} + \frac{3 s}{4 s} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{1 + 3 s}{4 s} = 0$

Step 6

Set the numerator equal to zero.

$1 + 3 s = 0$

Step 7

Solve the equation for $s$ .

Subtract $1$ from both sides of the equation.

$3 s = - 1$

Divide each term in $3 s = - 1$ by $3$ and simplify.

Divide each term in $3 s = - 1$ by $3$ .

$\frac{3 s}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 s}{3} = \frac{- 1}{3}$

Divide $s$ by $1$ .

$s = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$s = - \frac{1}{3}$

Solve by Factoring 5/(2s)+3/4=9/(4s)

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