Questions: Solve for x. x / (5x - 12) = 2 / x If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Solution Steps

We have the equation $\frac{x}{5x-12} = \frac{2}{x}$. Cross-multiplying gives $x \cdot x = 2(5x - 12)$.

Simplifying the equation, we get $x^2 = 10x - 24$. Rearranging the equation to form a quadratic equation, we have $x^2 - 10x + 24 = 0$.

We need to find two numbers that multiply to 24 and add up to -10. These numbers are -6 and -4. So, we can factor the quadratic equation as $(x - 6)(x - 4) = 0$.

Setting each factor to zero, we have two possible solutions: $x - 6 = 0 \Rightarrow x = 6$ $x - 4 = 0 \Rightarrow x = 4$

We need to ensure that neither solution makes the denominator of the original equation equal to zero. For $x=6$: $5x - 12 = 5(6) - 12 = 30 - 12 = 18 \neq 0$, and $x = 6 \neq 0$. For $x=4$: $5x - 12 = 5(4) - 12 = 20 - 12 = 8 \neq 0$, and $x = 4 \neq 0$. Both solutions are valid.

Final Answer