Question

Simplify the following expression.

(1/3x+4/7)+(2/3x+5/6)

Answer 1

To simplify the expression \((\frac{1}{3}x + \frac{4}{7}) + (\frac{2}{3}x + \frac{5}{6})\), we can start by combining like terms.

1. Combine the \(x\) terms:
\[
\frac{1}{3}x + \frac{2}{3}x = \left(\frac{1}{3} + \frac{2}{3}\right)x = \frac{3}{3}x = 1x = x
\]

2. Now, combine the constant terms:
\[
\frac{4}{7} + \frac{5}{6}
\]
To do this, we need a common denominator. The least common multiple of 7 and 6 is 42.

Rewrite each fraction with a denominator of 42:
\[
\frac{4}{7} = \frac{4 \times 6}{7 \times 6} = \frac{24}{42}
\]
\[
\frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42}
\]

Now, we can add the two fractions:
\[
\frac{24}{42} + \frac{35}{42} = \frac{24 + 35}{42} = \frac{59}{42}
\]

Putting it all together, we have:
\[
x + \frac{59}{42}
\]

Thus, the simplified expression is:
\[
\boxed{x + \frac{59}{42}}
\]