OPERATIONS WITH RATIONAL EXPRESSIONS WORKSHEET

Problem 1:

52 - 4v3v + 3

Problem 2 :

2k - 3 - 2k + 6

Problem 3 :

(n + 3)(n - 8)n - 8 · n - 85(n + 3)

Problem 4 :

2a(a - 7)2a(a + 5) · a + 5a + 6

Problem 5 :

5b2(b - 5)b - 5 ÷ 5b2(b - 3)4b2

Problem 6 :

10n2(n - 8)2 ÷ 3n(n + 2)(n - 8)2

Solutions

1. Answer 

Given, 52 - 4v3v + 3= 52 × 3v + 3 3v + 3- 4v3v + 3 × 22= 5(3v + 3)2(3v + 3) - 2(4v)2(3v + 3)= 5(3v + 3) - 8v2(3v + 3)= 15v + 15 - 8v6v + 6= 7v + 156v + 6

2. Answer 

Given, 2k - 3 - 2k + 6= 2k - 3 × k + 6k + 6 - 2k + 6 × k - 3k - 3= 2(k + 6)(k - 3)(k + 6) - 2(k - 3)(k + 6)(k - 3)= 2(k + 6) - 2(k - 3)(k - 3)(k + 6)= 2k + 12 - 2k + 6k2 + 6k - 3k - 18= 18k2 + 3k - 18

3. Answer 

Given, (n + 3)(n - 8)n - 8 · n - 85(n + 3)Cancel the common factor.=(n + 3)(n - 8)n - 8 · n - 85(n + 3)=n + 3 · n - 85n + 15= (n + 3)(n - 8)5n + 15 = (n + 3)(n - 8)5(n + 3)Cancel the common factor.= (n + 3)(n - 8)5(n + 3)= n - 85

4. Answer 

Given, 2a(a - 7)2a(a + 5) · a + 5a + 6 Cancel the common factor.= 2a(a - 7)2a(a + 5) · (a + 5)a + 6= a - 7a + 6

5. Answer 

Given, 5b2(b - 5)b - 5 ÷ 5b2(b - 3)4b2= 5b2(b - 5)b - 55b2(b - 3)4b2=5b2(b - 5)b - 5 × 4b25b2(b - 3)Cancel the common factor.=5b2 (b - 5)b - 5 × 4b25b2(b - 3)= 4b2b - 3

6. Answer 

Given, 10n2(n - 8)2 ÷ 3n(n + 2)(n - 8)2= 10n2(n - 8)23n(n + 2)(n - 8)2= 10n2(n - 8)2 × (n - 8)23n(n + 2)Cancel the common factor.= 10n2(n - 8)2 × (n - 8)23n(n + 2)= 10n23n(n + 2)= 10n3(n + 2)= 10n3n + 6

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