Question

Simplify the following expression.

(2/7x + 1/7) - (2/9x - 2/3)

Answer 1

To simplify the expression \((2/7x + 1/7) - (2/9x - 2/3)\), we first distribute the negative sign in front of the parentheses:

\[
(2/7x + 1/7) - (2/9x - 2/3) = 2/7x + 1/7 - 2/9x + 2/3
\]

Next, we can combine the \(x\) terms and constant terms separately.

1. **Combine \(x\) terms:**

\[
2/7x - 2/9x
\]

To combine these fractions, we need a common denominator, which is \(63\) (the least common multiple of \(7\) and \(9\)):

\[
2/7 = \frac{2 \cdot 9}{7 \cdot 9} = \frac{18}{63}
\]

\[
2/9 = \frac{2 \cdot 7}{9 \cdot 7} = \frac{14}{63}
\]

So,

\[
2/7x - 2/9x = \frac{18}{63}x - \frac{14}{63}x = \frac{4}{63}x
\]

2. **Combine constant terms:**

\[
1/7 + 2/3
\]

To combine these fractions, we again need a common denominator. The least common multiple of \(7\) and \(3\) is \(21\):

\[
1/7 = \frac{1 \cdot 3}{7 \cdot 3} = \frac{3}{21}
\]

\[
2/3 = \frac{2 \cdot 7}{3 \cdot 7} = \frac{14}{21}
\]

So,

\[
1/7 + 2/3 = \frac{3}{21} + \frac{14}{21} = \frac{17}{21}
\]

3. **Combine the results:**

Now, we can put everything together:

\[
\frac{4}{63}x + \frac{17}{21}
\]

Thus, the simplified expression is:

\[
\frac{4}{63}x + \frac{17}{21}
\]