Chapter 5.6, Problem 13WE

To determine

To simplify the given expression.

Answer to Problem 13WE

  $\frac{p^2+4q^2}{2p^3{q}^4}$

Explanation of Solution

Given:

Expression: $\frac{1}{2p{q}^4}+\frac{2}{p^3{q}^2}$

Calculation:

Consider the given expression $\frac{1}{2p{q}^4}+\frac{2}{p^3{q}^2}$ ,

Since the denominators of both the fractions are different, find the least common denominator for both the fractions.

Here, least common denominator is $2p^3{q}^4$ , so

  $\frac{1}{2p{q}^4}+\frac{2}{p^3{q}^2}$

  $=\frac{1\cdot p^2}{2p{q}^4\cdot p^2}+\frac{2\cdot 2q^2}{p^3{q}^2\cdot 2q^2}$

  $=\frac{p^2}{2p^3{q}^4}+\frac{4q^2}{2p^3{q}^4}$

Now, as the denominators of the two fractions are same, simply add the numerators and put the result on the same denominator.

  $=\frac{p^2+4q^2}{2p^3{q}^4}$

Conclusion:

Therefore, after simplification, the answer is $\frac{p^2+4q^2}{2p^3{q}^4}$ .