Practice worksheet for adding and subtracting rational expressions with algebraic fractions.

Let’s solve each problem step by step. We’re adding or subtracting rational expressions (fractions with variables or numbers). The key is: if denominators are the same, just add/subtract numerators. If not, find a common denominator first.

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Problem 1:
$\frac{7}{8} + \frac{1}{8}$
Same denominator → add numerators: $7 + 1 = 8$
So: $\frac{8}{8} = 1$

✔ Final for #1: 1

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Problem 2:
$\frac{9}{13} - \frac{5}{13}$
Same denominator → subtract numerators: $9 - 5 = 4$
So: $\frac{4}{13}$ — already simplified.

✔ Final for #2: $\frac{4}{13}$

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Problem 3:
$\frac{11}{20} - \frac{3}{20}$
Same denominator → $11 - 3 = 8$ → $\frac{8}{20}$
Simplify: divide numerator and denominator by 4 → $\frac{2}{5}$

✔ Final for #3: $\frac{2}{5}$

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Problem 4:
$\frac{8}{11} + \frac{3}{11}$
Same denominator → $8 + 3 = 11$ → $\frac{11}{11} = 1$

✔ Final for #4: 1

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Problem 5:
$\frac{x}{x^2} + \frac{y}{x^2}$
Same denominator → combine numerators: $\frac{x + y}{x^2}$
Can we simplify? Not unless x+y shares factor with x² — no info, so leave as is.

But wait — $\frac{x}{x^2} = \frac{1}{x}$, but since both terms have same denominator, better to keep combined.

Actually, let’s check:
$\frac{x + y}{x^2}$ — this is simplest form unless told otherwise.

✔ Final for #5: $\frac{x + y}{x^2}$

Wait — maybe they want it split? No, instruction says “combine like terms in numerator” — so yes, $\frac{x + y}{x^2}$ is correct.

BUT — note: $\frac{x}{x^2} = \frac{1}{x}$, and $\frac{y}{x^2}$ stays — but that would be different denominators. Since original has same denominator, we must combine numerators.

So yes: $\frac{x + y}{x^2}$

However, sometimes you can reduce if possible — here, no common factors between (x+y) and x² unless specified. So leave as is.

✔ Still: $\frac{x + y}{x^2}$

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Problem 6:
$\frac{8}{x} + \frac{x}{x}$
Second term: $\frac{x}{x} = 1$, but let’s do it properly.

Common denominator is x.

First term: $\frac{8}{x}$
Second term: $\frac{x}{x} = \frac{x}{x}$ → so total: $\frac{8 + x}{x}$

Which is $\frac{x + 8}{x}$ — can write as $1 + \frac{8}{x}$, but instructions say “simplified form” — usually meaning single fraction unless specified.

Check: $\frac{8 + x}{x} = \frac{x + 8}{x}$ — that’s fine.

Is it reducible? Only if x divides x+8 — which it doesn’t generally. So leave as $\frac{x + 8}{x}$

Alternatively, some might prefer splitting: $1 + \frac{8}{x}$ — but the problem says “add or subtract... combining like terms in the numerator” — so probably expects single fraction.

Looking at other problems, they kept single fractions. So:

✔ Final for #6: $\frac{x + 8}{x}$

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Problem 7:
$\frac{12}{7} + \frac{5}{7} + \frac{8}{7}$
All same denominator → add numerators: $12 + 5 + 8 = 25$
So: $\frac{25}{7}$ — improper fraction, but acceptable unless mixed number required. Problem doesn’t specify, so leave as is.

✔ Final for #7: $\frac{25}{7}$

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Problem 8:
$\frac{7p}{10} + \frac{7p}{10}$
Same denominator → $7p + 7p = 14p$ → $\frac{14p}{10}$
Simplify: divide numerator and denominator by 2 → $\frac{7p}{5}$

✔ Final for #8: $\frac{7p}{5}$

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Problem 9:
$\frac{7}{2a} + \frac{3}{2a} + \frac{4}{2a}$
Same denominator → add numerators: $7 + 3 + 4 = 14$ → $\frac{14}{2a}$
Simplify: divide numerator and denominator by 2 → $\frac{7}{a}$

✔ Final for #9: $\frac{7}{a}$

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Problem 10:
$\frac{9}{5a} - \frac{5}{5a}$
Same denominator → $9 - 5 = 4$ → $\frac{4}{5a}$ — already simplified.

✔ Final for #10: $\frac{4}{5a}$

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Now, compiling all final answers:

Final Answer:
1. 1
2. $\frac{4}{13}$
3. $\frac{2}{5}$
4. 1
5. $\frac{x + y}{x^2}$
6. $\frac{x + 8}{x}$
7. $\frac{25}{7}$
8. $\frac{7p}{5}$
9. $\frac{7}{a}$
10. $\frac{4}{5a}$