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Express in its simplest form: $$\frac{5-x}{5} + \frac{x-4}{4}$$ - Junior Cycle Mathematics - Question (a) - 2013

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Question (a)

Express-in-its-simplest-form:--$$\frac{5-x}{5}-+-\frac{x-4}{4}$$-Junior Cycle Mathematics-Question (a)-2013.png

Express in its simplest form: $$\frac{5-x}{5} + \frac{x-4}{4}$$

Worked Solution & Example Answer:Express in its simplest form: $$\frac{5-x}{5} + \frac{x-4}{4}$$ - Junior Cycle Mathematics - Question (a) - 2013

Step 1

Combine the Fractions

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Answer

To combine the fractions, find a common denominator. The denominators are 5 and 4, so the least common multiple is 20. Rewrite each fraction:

5x5=4(5x)20\frac{5-x}{5} = \frac{4(5-x)}{20}

x44=5(x4)20\frac{x-4}{4} = \frac{5(x-4)}{20}

Now we can combine them:

4(5x)+5(x4)20\frac{4(5-x) + 5(x-4)}{20}

Step 2

Simplify the Numerator

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Answer

Expand the expression in the numerator:

4(5x)+5(x4)=204x+5x204(5-x) + 5(x-4) = 20 - 4x + 5x - 20

This simplifies to:

(2020)+x20=x20\frac{(20 - 20) + x}{20} = \frac{x}{20}

Step 3

Final Answer

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Answer

Thus, the final answer in simplest form is:

x20\frac{x}{20}

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