Chapter 8.3, Problem 1MRE

To determine

To calculate: Thesimplified form of,

  $\frac{x+3}{3}+\frac{x}{2}=0$

Answer to Problem 1MRE

The simplified form of $\frac{x+3}{3}+\frac{x}{2}=0$ is $-\frac{6}{5}$ .

Explanation of Solution

Given information:

The given statement is as:

  $\frac{x+3}{3}+\frac{x}{2}=0$

Formula used:

When two or more functions with different denominators are added or subtracted then take LCM of the denominator and then with the result of the LCM, by the result divide the denominator and then the result multiply by the numerator.

Calculation:

Consider the equation,

  $\frac{x+3}{3}+\frac{x}{2}=0$

When two or more functions with different denominators are added or subtracted then take LCM of the denominator and then with the result of the LCM, by the result divide the denominator and then the result multiply by the numerator.

so the given expression can be written as,

  $\begin{array}{c}\frac{x+3}{3}+\frac{x}{2}=0\\ \frac{2\left(x+3\right)+3\left(x\right)}{6}=0\\ \frac{2x+6+3x}{6}=0\\ 5x+6=0\end{array}$

To get the value of $x$:

  $\begin{array}{c}5x+6=0\\ 5x=-6\\ x=\frac{-6}{5}\end{array}$

Since, $-\frac{6}{5}$ cannot be simplified further,

Hence, the simplified form of $\frac{x+3}{3}+\frac{x}{2}=0$ is $-\frac{6}{5}$ .