Question
2) \( \frac{3}{8 p^{2} r}+\frac{5}{4 p^{2} r} \)
Ask by Montgomery Elliott. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{13}{8p^{2}r} \).
Solution
We start with the given expression:
(3 / (8p²r)) + (5 / (4p²r))
Notice that the denominators are 8p²r and 4p²r. To add these fractions, we need a common denominator. The least common denominator here is 8p²r.
Rewrite the second fraction with the common denominator of 8p²r:
5/(4p²r) = (5 × 2)/(4p²r × 2) = 10/(8p²r)
Now the expression becomes:
(3/(8p²r)) + (10/(8p²r))
Since the denominators are the same, add the numerators:
(3 + 10) / (8p²r) = 13/(8p²r)
Therefore, the simplified expression is:
13/(8p²r)
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Simplify this solution Mind Expander
To combine the fractions \( \frac{3}{8 p^{2} r} \) and \( \frac{5}{4 p^{2} r} \), we first need a common denominator. The least common multiple of the denominators \( 8 p^{2} r \) and \( 4 p^{2} r \) is \( 8 p^{2} r \). Now, we can rewrite \( \frac{5}{4 p^{2} r} \) to have the common denominator: \[ \frac{5}{4 p^{2} r} = \frac{5 \cdot 2}{4 \cdot 2 \cdot p^{2} r} = \frac{10}{8 p^{2} r} \] Now we can add the two fractions: \[ \frac{3}{8 p^{2} r} + \frac{10}{8 p^{2} r} = \frac{3 + 10}{8 p^{2} r} = \frac{13}{8 p^{2} r} \] Thus, the combined fraction is: \[ \frac{13}{8 p^{2} r} \]
