Question

solve the following rational equation and simplify your answer.\\(\frac{x + 1}{7x} = \frac{x - 2}{6x}\\)\
answer\
separate multiple answers with commas.\
\\(x = \\)

Explanation:

Step1: Eliminate denominators

Multiply both sides by the least common multiple of $7x$ and $6x$, which is $42x$ (note $x
eq 0$):
$$42x \cdot \frac{x+1}{7x} = 42x \cdot \frac{x-2}{6x}$$
Simplify to get:
$$6(x+1) = 7(x-2)$$

Step2: Expand both sides

Distribute the coefficients:
$$6x + 6 = 7x - 14$$

Step3: Isolate the variable $x$

Subtract $6x$ from both sides, then add 14 to both sides:
$$6 + 14 = 7x - 6x$$
$$20 = x$$

Answer:

$x = 20$