Solve by Factoring 1/(4x)-3/4=7/x

$\frac{1}{4 x} - \frac{3}{4} = \frac{7}{x}$

Step 1

Subtract $\frac{7}{x}$ from both sides of the equation.

$\frac{1}{4 x} - \frac{3}{4} - \frac{7}{x} = 0$

Step 2

Simplify $\frac{1}{4 x} - \frac{3}{4} - \frac{7}{x}$ .

To write $- \frac{7}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4 x} - \frac{7}{x} \cdot \frac{4}{4} - \frac{3}{4} = 0$

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

Multiply $\frac{7}{x}$ by $\frac{4}{4}$ .

$\frac{1}{4 x} - \frac{7 \cdot 4}{x \cdot 4} - \frac{3}{4} = 0$

Reorder the factors of $x \cdot 4$ .

$\frac{1}{4 x} - \frac{7 \cdot 4}{4 x} - \frac{3}{4} = 0$

Combine the numerators over the common denominator.

$\frac{1 - 7 \cdot 4}{4 x} - \frac{3}{4} = 0$

Simplify the numerator.

Multiply $- 7$ by $4$ .

$\frac{1 - 28}{4 x} - \frac{3}{4} = 0$

Subtract $28$ from $1$ .

$\frac{- 27}{4 x} - \frac{3}{4} = 0$

Move the negative in front of the fraction.

$- \frac{27}{4 x} - \frac{3}{4} = 0$

Step 3

Factor $- 1$ out of $- \frac{27}{4 x} - \frac{3}{4}$ .

Factor $- 1$ out of $- \frac{27}{4 x}$ .

$- (\frac{27}{4 x}) - \frac{3}{4} = 0$

Factor $- 1$ out of $- \frac{3}{4}$ .

$- (\frac{27}{4 x}) - (\frac{3}{4}) = 0$

Factor $- 1$ out of $- (\frac{27}{4 x}) - (\frac{3}{4})$ .

$- (\frac{27}{4 x} + \frac{3}{4}) = 0$

Step 4

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

$- (\frac{27}{4 x} + \frac{3}{4} \cdot \frac{x}{x}) = 0$

Step 5

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

$- (\frac{27}{4 x} + \frac{3 x}{4 x}) = 0$

Step 6

Combine the numerators over the common denominator.

$- \frac{27 + 3 x}{4 x} = 0$

Step 7

Factor $3$ out of $27 + 3 x$ .

Factor $3$ out of $27$ .

$- \frac{3 \cdot 9 + 3 x}{4 x} = 0$

Factor $3$ out of $3 \cdot 9 + 3 x$ .

$- \frac{3 \cdot (9 + x)}{4 x} = 0$

Multiply $3$ by $9 + x$ .

$- \frac{3 (9 + x)}{4 x} = 0$

Step 8

Set the numerator equal to zero.

$3 (9 + x) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $3 (9 + x) = 0$ by $3$ and simplify.

Divide each term in $3 (9 + x) = 0$ by $3$ .

$\frac{3 (9 + x)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (9 + x)}{3} = \frac{0}{3}$

Divide $9 + x$ by $1$ .

$9 + x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$9 + x = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Solve by Factoring 1/(4x)-3/4=7/x

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