Chapter 8, Problem 7PT

To determine

To simplify: The expression $\frac{1}{y}+\frac{2}{7}-\frac{3}{2y^2}$ .

Answer to Problem 7PT

The simplified expression is $\frac{4y^2+14y-21}{14y^2}$ .

Explanation of Solution

Given information:

The expression is $\frac{1}{y}+\frac{2}{7}-\frac{3}{2y^2}$ .

Calculation:

To simplify the expression, find the least common denominator (LCD). Rewrite each expression with the LCD then simplify. Therefore,

  $\begin{array}{l}\frac{1}{y}+\frac{2}{7}-\frac{3}{2y^2}=\frac{1}{y}\cdot \frac{14y}{14y}+\frac{2}{7}\cdot \frac{2y^2}{2y^2}-\frac{3}{2y^2}\cdot \frac{7}{7}\text{ (LCD is }14y^2\text{)}\\ \frac{1}{y}+\frac{2}{7}-\frac{3}{2y^2}=\frac{14y}{14y^2}+\frac{4y^2}{14y^2}-\frac{21}{14y^2}\text{ (Multiply fraction)}\\ \frac{1}{y}+\frac{2}{7}-\frac{3}{2y^2}=\frac{14y+4y^2-21}{14y^2}\text{ (Simplify numerator)}\\ \frac{1}{y}+\frac{2}{7}-\frac{3}{2y^2}=\frac{4y^2+14y-21}{14y^2}\end{array}$

Hence,

The simplified expression is $\frac{4y^2+14y-21}{14y^2}$ .