Solve by Factoring 4/x=9/5-(7x-4)/(5x)

$\frac{4}{x} = \frac{9}{5} - \frac{7 x - 4}{5 x}$

Step 1

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

Subtract $\frac{9}{5}$ from both sides of the equation.

$\frac{4}{x} - \frac{9}{5} = - \frac{7 x - 4}{5 x}$

Add $\frac{7 x - 4}{5 x}$ to both sides of the equation.

$\frac{4}{x} - \frac{9}{5} + \frac{7 x - 4}{5 x} = 0$

Step 2

Simplify $\frac{4}{x} - \frac{9}{5} + \frac{7 x - 4}{5 x}$ .

To write $\frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{x} \cdot \frac{5}{5} + \frac{7 x - 4}{5 x} - \frac{9}{5} = 0$

Write each expression with a common denominator of $x \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 5}{x \cdot 5} + \frac{7 x - 4}{5 x} - \frac{9}{5} = 0$

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

$\frac{4 \cdot 5}{5 x} + \frac{7 x - 4}{5 x} - \frac{9}{5} = 0$

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 7 x - 4}{5 x} - \frac{9}{5} = 0$

Multiply $4$ by $5$ .

$\frac{20 + 7 x - 4}{5 x} - \frac{9}{5} = 0$

Subtract $4$ from $20$ .

$\frac{7 x + 16}{5 x} - \frac{9}{5} = 0$

To write $- \frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{7 x + 16}{5 x} - \frac{9}{5} \cdot \frac{x}{x} = 0$

Multiply $\frac{9}{5}$ by $\frac{x}{x}$ .

$\frac{7 x + 16}{5 x} - \frac{9 x}{5 x} = 0$

Combine the numerators over the common denominator.

$\frac{7 x + 16 - 9 x}{5 x} = 0$

Simplify the numerator.

Subtract $9 x$ from $7 x$ .

$\frac{- 2 x + 16}{5 x} = 0$

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

Factor $2$ out of $- 2 x$ .

$\frac{2 (- x) + 16}{5 x} = 0$

Factor $2$ out of $16$ .

$\frac{2 (- x) + 2 (8)}{5 x} = 0$

Factor $2$ out of $2 (- x) + 2 (8)$ .

$\frac{2 (- x + 8)}{5 x} = 0$

Factor $- 1$ out of $- x$ .

$\frac{2 (- (x) + 8)}{5 x} = 0$

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{2 (- (x) - 1 (- 8))}{5 x} = 0$

Factor $- 1$ out of $- (x) - 1 (- 8)$ .

$\frac{2 (- (x - 8))}{5 x} = 0$

Rewrite $- (x - 8)$ as $- 1 (x - 8)$ .

$\frac{2 (- 1 (x - 8))}{5 x} = 0$

Move the negative in front of the fraction.

$- \frac{2 (x - 8)}{5 x} = 0$

Step 3

Set the numerator equal to zero.

$2 (x - 8) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (x - 8) = 0$ by $2$ and simplify.

Divide each term in $2 (x - 8) = 0$ by $2$ .

$\frac{2 (x - 8)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x - 8)}{2} = \frac{0}{2}$

Divide $x - 8$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Solve by Factoring 4/x=9/5-(7x-4)/(5x)

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