to solve the equation (\frac{x-1}{2} \frac{x 1}{3} = \frac{1}{2}), follow these steps:
step 1: eliminate denominators
the least common denominator (lcd) of 2 and 3 is 6. multiply every term by 6:
[6 \cdot \frac{x-1}{2} 6 \cdot \frac{x 1}{3} = 6 \cdot \frac{1}{2}]
step 2: simplify each term
[3(x-1) 2(x 1) = 3]
step 3: expand and combine like terms
[3x - 3 2x 2 = 3]
[5x - 1 = 3]
step 4: solve for (x)
add 1 to both sides:
[5x = 4]
divide by 5:
[x = \frac{4}{5}]
answer: (\boxed{\dfrac{4}{5}})
作者声明:本文包含人工智能生成内容。
