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

Question (a)

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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

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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:

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

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

Now we can combine them:

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

Step 2

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Answer

Expand the expression in the numerator:

$4(5-x) + 5(x-4) = 20 - 4x + 5x - 20$

This simplifies to:

$\frac{(20 - 20) + x}{20} = \frac{x}{20}$

Step 3

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Answer

Thus, the final answer in simplest form is:

$\frac{x}{20}$

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