b. ((3)/(2)+(2)/(3)-(5)/(6))/((7)/(36)+(1)/(4)+(8)/(9))

Find Common Denominator: First, we need to simplify the numerator of the expression: (3/2) + (2/3) - (5/6). To do this, we find a common denominator for the fractions, which is 6.Convert Numerators to Common Denominator: Now we convert each fraction in the numerator to have the common denominator of 6. This gives us (9/6) + (4/6) - (5/6).Simplify Numerator: Next, we add and subtract the numerators: 9 + 4 - 5 = 8. So the numerator simplifies to 8/6, which can be further simplified to 4/3 by dividing both the numerator and the denominator by 2.Find Common Denominator for Denominator: Now we simplify the denominator of the expression: (7/36) + (1/4) + (8/9). We need to find a common denominator for these fractions, which is 36.Convert Denominators to Common Denominator: We convert each fraction in the denominator to have the common denominator of 36. This gives us (7/36) + (9/36) + (32/36).Simplify Denominator: Next, we add the numerators: 7 + 9 + 32 = 48. So the denominator simplifies to 48/36, which can be further simplified to 4/3 by dividing both the numerator and the denominator by 12.Divide Fractions: Now we have the simplified numerator and denominator: (4/3) / (4/3). When we divide two fractions that are the same, the result is 1.Final Simplified Form: The final simplified form of the expression is 1. This answers the question prompt.

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b. $\frac{3}{2}+\frac{2}{3}-\frac{5}{6}$ / $\frac{7}{36}+\frac{1}{4}+\frac{8}{9}$

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Q. b.

\frac{3}{2}+\frac{2}{3}-\frac{5}{6}

\frac{7}{36}+\frac{1}{4}+\frac{8}{9}

Find Common Denominator: First, we need to simplify the numerator of the expression: $(\frac{3}{2}) + (\frac{2}{3}) - (\frac{5}{6})$ . To do this, we find a common denominator for the fractions, which is $6$ .
Convert Numerators to Common Denominator: Now we convert each fraction in the numerator to have the common denominator of $6$ . This gives us $(\frac{9}{6}) + (\frac{4}{6}) - (\frac{5}{6})$ .
Simplify Numerator: Next, we add and subtract the numerators: $9 + 4 - 5 = 8$ . So the numerator simplifies to $\frac{8}{6}$ , which can be further simplified to $\frac{4}{3}$ by dividing both the numerator and the denominator by $2$ .
Find Common Denominator for Denominator: Now we simplify the denominator of the expression: $(\frac{7}{36}) + (\frac{1}{4}) + (\frac{8}{9})$ . We need to find a common denominator for these fractions, which is $36$ .
Convert Denominators to Common Denominator: We convert each fraction in the denominator to have the common denominator of $36$ . This gives us $(\frac{7}{36}) + (\frac{9}{36}) + (\frac{32}{36})$ .
Simplify Denominator: Next, we add the numerators: $7 + 9 + 32 = 48$ . So the denominator simplifies to $\frac{48}{36}$ , which can be further simplified to $\frac{4}{3}$ by dividing both the numerator and the denominator by $12$ .
Divide Fractions: Now we have the simplified numerator and denominator: $(\frac{4}{3}) / (\frac{4}{3})$ . When we divide two fractions that are the same, the result is $1$ .
Final Simplified Form: The final simplified form of the expression is $1$ . This answers the question prompt.