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Write the following as a single fraction in its simplest form - Junior Cycle Mathematics - Question c - 2011

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Question c

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Write the following as a single fraction in its simplest form. $$\frac{x+2}{3} - \frac{x-3}{4}$$

Worked Solution & Example Answer:Write the following as a single fraction in its simplest form - Junior Cycle Mathematics - Question c - 2011

Step 1

Step 1: Find a common denominator

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Answer

The denominators are 3 and 4. The least common multiple (LCM) is 12.

Step 2

Step 2: Rewrite each fraction with the common denominator

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Answer

x+23=4(x+2)12\frac{x+2}{3} = \frac{4(x+2)}{12} and x−34=3(x−3)12\frac{x-3}{4} = \frac{3(x-3)}{12}.

Step 3

Step 3: Subtract the fractions

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Answer

4(x+2)−3(x−3)12\frac{4(x+2) - 3(x-3)}{12}

Step 4

Step 4: Simplify the numerator

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Answer

Expanding gives us: 4x+8−3x+9=(4x−3x)+(8+9)=x+174x + 8 - 3x + 9 = (4x - 3x) + (8 + 9) = x + 17.

Step 5

Step 5: Final answer

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Answer

x+1712\frac{x + 17}{12}.

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