Answer: (b) ((h-1))/(2)+((h-2))/(3)=3

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. The common denominator for 2 and 3 is 6.Rewrite Fractions: Rewrite each fraction with the common denominator. ((h-1))/2 * (3/3) + ((h-2))/3 * (2/2) = 3 This becomes (3(h-1))/6 + (2(h-2))/6 = 3Combine Fractions: Combine the fractions on the left side since they have the same denominator. (3(h-1) + 2(h-2))/6 = 3Distribute and Combine: Distribute the numerators and combine like terms. (3h - 3 + 2h - 4)/6 = 3 This simplifies to (5h - 7)/6 = 3Eliminate Denominator: Multiply both sides of the equation by 6 to eliminate the denominator. (5h - 7)/6 * 6 = 3 * 6 This simplifies to 5h - 7 = 18Isolate h Term: Add 7 to both sides of the equation to isolate the term with h. 5h - 7 + 7 = 18 + 7 This simplifies to 5h = 25Solve for h: Divide both sides by 5 to solve for h. 5h/5 = 25/5 This simplifies to h = 5

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Answer: $\newline$ (b) $\frac{(h-1)}{2}+\frac{(h-2)}{3}=3$

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Algebra 2

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Q. Answer:

\newline

(b)

\frac{(h-1)}{2}+\frac{(h-2)}{3}=3

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. $\newline$ The common denominator for $2$ and $3$ is $6$ .
Rewrite Fractions: Rewrite each fraction with the common denominator. $\newline$ $\frac{h-1}{2} \times \frac{3}{3} + \frac{h-2}{3} \times \frac{2}{2} = 3$ $\newline$ This becomes $\frac{3(h-1)}{6} + \frac{2(h-2)}{6} = 3$
Combine Fractions: Combine the fractions on the left side since they have the same denominator. $\frac{3(h-1) + 2(h-2)}{6} = 3$
Distribute and Combine: Distribute the numerators and combine like terms. $\newline$ $(3h - 3 + 2h - 4)/6 = 3$ $\newline$ This simplifies to $(5h - 7)/6 = 3$
Eliminate Denominator: Multiply both sides of the equation by $6$ to eliminate the denominator. $\newline$ $(5h - 7)/6 \times 6 = 3 \times 6$ $\newline$ This simplifies to $5h - 7 = 18$
Isolate h Term: Add $7$ to both sides of the equation to isolate the term with $h$ . $\newline$ $5h - 7 + 7 = 18 + 7$ $\newline$ This simplifies to $5h = 25$
Solve for $h$ : Divide both sides by $5$ to solve for $h$ . $\frac{5h}{5} = \frac{25}{5}$ This simplifies to $h = 5$