Question

solve for the variable. \\(\frac{6}{2h} - \frac{3}{2} = \frac{6}{h}\\)\\(\bigcirc\\ h = -2\\)\\(\bigcirc\\ h = 3\\)\\(\bigcirc\\ h = -6\\)\\(\bigcirc\\ h = -4\\)

Explanation:

Step1: Find common denominator

The equation is $\frac{6}{2h} - \frac{3}{2} = \frac{6}{h}$. The common denominator of $2h$, $2$, and $h$ is $2h$. Multiply each term by $2h$ to eliminate denominators:
$$\frac{6}{2h} \times 2h - \frac{3}{2} \times 2h = \frac{6}{h} \times 2h$$

Step2: Simplify each term

Simplify each term:

• $\frac{6}{2h} \times 2h = 6$
• $\frac{3}{2} \times 2h = 3h$
• $\frac{6}{h} \times 2h = 12$

So the equation becomes $6 - 3h = 12$.

Step3: Solve for h

Subtract 6 from both sides:
$$-3h = 12 - 6$$
$$-3h = 6$$
Divide both sides by -3:
$$h = \frac{6}{-3}$$
$$h = -2$$

Answer:

$h = -2$ (corresponding to the option "h = -2")