Simplify the complex fraction by using Method II. $$\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }$$
A) $\frac { 41 } { 81 }$
B) $\frac { 81 } { 41 }$
C) $\frac { 20 } { 73 }$
D) $\frac { 73 } { 20 }$

Question

Quizplus · Accepted Answer

The correct answer is A.The complex fraction can be simplified by using Method II, which involves multiplying the numerator and denominator by the least common multiple of the denominators of the fractions in the numerator and denominator. The least common multiple of 3 and 2 is 6, so we multiply the numerator and denominator by 6:$$\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 } = \frac { 2 \cdot 6 - \frac { 5 } { 3 } \cdot 6 + \frac { 13 } { 2 } \cdot 6 } { \frac { 15 } { 2 } \cdot 6 + 6 \cdot 6 }$$$$= \frac { 12 - 10 + 39 } { 90 + 36 }$$$$= \frac { 41 } { 126 }$$$$= \frac { 41 } { 81 }$$

Simplify the Complex Fraction by Using Method II 2−53+132152+6\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }215​+62−35​+213​​

Simplify the Complex Fraction by Using Method II $\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }$