Question

question 3 of 10, step 1 of 1 solve the following rational equation and simplify your answer. \\(\frac{9}{5x} - \frac{1}{8} = \frac{3}{4x}\\) answer how to enter your answer (opens in new window) separate multiple answers with commas. if the equation has no solution, indicate
o solution\. selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. \\(x = \\) \\(\circ\\) no solution

Explanation:

Step1: Find common denominator

The denominators are $5x$, $8$, and $4x$. The least common denominator is $40x$.

Step2: Multiply all terms by LCD

$$40x \cdot \frac{9}{5x} - 40x \cdot \frac{1}{8} = 40x \cdot \frac{3}{4x}$$
Simplify each term:
$72 - 5x = 30$

Step3: Isolate the variable term

Subtract 72 from both sides:
$$-5x = 30 - 72$$
$$-5x = -42$$

Step4: Solve for x

Divide both sides by $-5$:
$$x = \frac{-42}{-5} = \frac{42}{5}$$

Step5: Verify solution

Substitute $x=\frac{42}{5}$ into original equation: denominators $5x=42$, $4x=\frac{168}{5}$ are non-zero, so the solution is valid.

Answer:

$x = \frac{42}{5}$